Publications

Molecular Beam Epitaxy of Homogeneous Topological HgTe on Doped InAs Substrate. Biswas, Mahitosh; Fürst, Lena; Kamp, Martin; Schreyeck, Steffen; Buhmann, Hartmut; Molenkamp, Laurens W. In Advanced Functional Materials, 35(3). Wiley, 2024.
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HgTe has been considered to be one of the most versatile topological materials. Depending on the in-plane strain, Weyl and Dirac semi-metal, as well as topological insulator phases, are feasible. Here, for the first time it is reported, that an InAs:S substrate promotes an initial 2D growth of a ZnTe thin layer and subsequent high crystalline quality ZnTe/CdTe superlattices serve as a smooth and continuous virtual substrate for the growth of (Cd,Hg)Te/HgTe/(Cd,Hg)Te heterostructures with unstrained quantum well HgTe (topological insulator) and compressively strained bulk HgTe (Weyl semimetal) by molecular beam epitaxy. Compared with the superlattices previously grown on GaAs substrates, the quantum well and bulk heterostructures exhibit homogeneous surfaces with root mean square roughnesses of 0.88–0.93 nm, which is three times lower than those observed for 3D islands (2.7–3.4 nm) on GaAs substrates. Additionally, magnetotransport measurements confirm high electronic quality and demonstrate that the S-doped InAs substrate can be used as an effective back gate. These results manifest a (big) step forward toward the improvement of micro- and nanometer-sized top- and back-gated device fabrication on topological materials.

@article{Biswas_2024, abstract = {HgTe has been considered to be one of the most versatile topological materials. Depending on the in-plane strain, Weyl and Dirac semi-metal, as well as topological insulator phases, are feasible. Here, for the first time it is reported, that an InAs:S substrate promotes an initial 2D growth of a ZnTe thin layer and subsequent high crystalline quality ZnTe/CdTe superlattices serve as a smooth and continuous virtual substrate for the growth of (Cd,Hg)Te/HgTe/(Cd,Hg)Te heterostructures with unstrained quantum well HgTe (topological insulator) and compressively strained bulk HgTe (Weyl semimetal) by molecular beam epitaxy. Compared with the superlattices previously grown on GaAs substrates, the quantum well and bulk heterostructures exhibit homogeneous surfaces with root mean square roughnesses of 0.88–0.93 nm, which is three times lower than those observed for 3D islands (2.7–3.4 nm) on GaAs substrates. Additionally, magnetotransport measurements confirm high electronic quality and demonstrate that the S-doped InAs substrate can be used as an effective back gate. These results manifest a (big) step forward toward the improvement of micro- and nanometer-sized top- and back-gated device fabrication on topological materials.}, author = {Biswas, Mahitosh and Fürst, Lena and Kamp, Martin and Schreyeck, Steffen and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Advanced Functional Materials}, keywords = {qt}, month = {09}, number = 3, publisher = {Wiley}, title = {Molecular Beam Epitaxy of Homogeneous Topological HgTe on Doped InAs Substrate}, volume = 35, year = 2024 }

%0 Journal Article %1 Biswas_2024 %A Biswas, Mahitosh %A Fürst, Lena %A Kamp, Martin %A Schreyeck, Steffen %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2024 %I Wiley %J Advanced Functional Materials %N 3 %R 10.1002/adfm.202413229 %T Molecular Beam Epitaxy of Homogeneous Topological HgTe on Doped InAs Substrate %V 35 %X HgTe has been considered to be one of the most versatile topological materials. Depending on the in-plane strain, Weyl and Dirac semi-metal, as well as topological insulator phases, are feasible. Here, for the first time it is reported, that an InAs:S substrate promotes an initial 2D growth of a ZnTe thin layer and subsequent high crystalline quality ZnTe/CdTe superlattices serve as a smooth and continuous virtual substrate for the growth of (Cd,Hg)Te/HgTe/(Cd,Hg)Te heterostructures with unstrained quantum well HgTe (topological insulator) and compressively strained bulk HgTe (Weyl semimetal) by molecular beam epitaxy. Compared with the superlattices previously grown on GaAs substrates, the quantum well and bulk heterostructures exhibit homogeneous surfaces with root mean square roughnesses of 0.88–0.93 nm, which is three times lower than those observed for 3D islands (2.7–3.4 nm) on GaAs substrates. Additionally, magnetotransport measurements confirm high electronic quality and demonstrate that the S-doped InAs substrate can be used as an effective back gate. These results manifest a (big) step forward toward the improvement of micro- and nanometer-sized top- and back-gated device fabrication on topological materials.
Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells. Liang, Xianhu; Shamim, Saquib; Chen, Dongyun; Fürst, Lena; Taniguchi, Takashi; Watanabe, Kenji; Buhmann, Hartmut; Kleinlein, Johannes; Molenkamp, Laurens W. In Nanotechnology, 35(34), p. 345001. IOP Publishing, 2024.
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@article{Liang_2024, author = {Liang, Xianhu and Shamim, Saquib and Chen, Dongyun and Fürst, Lena and Taniguchi, Takashi and Watanabe, Kenji and Buhmann, Hartmut and Kleinlein, Johannes and Molenkamp, Laurens W}, journal = {Nanotechnology}, keywords = {qt}, month = {06}, number = 34, pages = 345001, publisher = {IOP Publishing}, title = {Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells}, volume = 35, year = 2024 }

%0 Journal Article %1 Liang_2024 %A Liang, Xianhu %A Shamim, Saquib %A Chen, Dongyun %A Fürst, Lena %A Taniguchi, Takashi %A Watanabe, Kenji %A Buhmann, Hartmut %A Kleinlein, Johannes %A Molenkamp, Laurens W %D 2024 %I IOP Publishing %J Nanotechnology %N 34 %P 345001 %R 10.1088/1361-6528/ad501c %T Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells %V 35
Overlapping top gate electrodes based on low temperature atomic layer deposition for nanoscale ambipolar lateral junctions. Fuchs, Christopher; Fürst, Lena; Buhmann, Hartmut; Kleinlein, Johannes; Molenkamp, Laurens W. In Nano Futures, 8(2), p. 025001. IOP Publishing, 2024.
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We present overlapping top gate electrodes for the formation of gate defined lateral junctions in semiconducting layers as an alternative to the back gate/top gate combination and to the split gate configuration. The optical lithography microfabrication of the overlapping top gates is based on multiple layers of low-temperature atomic layer deposited hafnium oxide, which acts as a gate dielectric and as a robust insulating layer between two overlapping gate electrodes exhibiting a large dielectric breakdown field of . The advantage of overlapping gates over the split gate approach is confirmed in model calculations of the electrostatics of the gate stack. The overlapping gate process is applied to Hall bar devices of mercury telluride in order to study the interaction of different quantum Hall states in the nn′, np, pn and pp′ regime.

@article{Fuchs_2024, abstract = {We present overlapping top gate electrodes for the formation of gate defined lateral junctions in semiconducting layers as an alternative to the back gate/top gate combination and to the split gate configuration. The optical lithography microfabrication of the overlapping top gates is based on multiple layers of low-temperature atomic layer deposited hafnium oxide, which acts as a gate dielectric and as a robust insulating layer between two overlapping gate electrodes exhibiting a large dielectric breakdown field of . The advantage of overlapping gates over the split gate approach is confirmed in model calculations of the electrostatics of the gate stack. The overlapping gate process is applied to Hall bar devices of mercury telluride in order to study the interaction of different quantum Hall states in the nn′, np, pn and pp′ regime.}, author = {Fuchs, Christopher and Fürst, Lena and Buhmann, Hartmut and Kleinlein, Johannes and Molenkamp, Laurens W}, journal = {Nano Futures}, keywords = {qt}, month = {05}, number = 2, pages = {025001}, publisher = {IOP Publishing}, title = {Overlapping top gate electrodes based on low temperature atomic layer deposition for nanoscale ambipolar lateral junctions}, volume = 8, year = 2024 }

%0 Journal Article %1 Fuchs_2024 %A Fuchs, Christopher %A Fürst, Lena %A Buhmann, Hartmut %A Kleinlein, Johannes %A Molenkamp, Laurens W %D 2024 %I IOP Publishing %J Nano Futures %N 2 %P 025001 %R 10.1088/2399-1984/ad4c33 %T Overlapping top gate electrodes based on low temperature atomic layer deposition for nanoscale ambipolar lateral junctions %V 8 %X We present overlapping top gate electrodes for the formation of gate defined lateral junctions in semiconducting layers as an alternative to the back gate/top gate combination and to the split gate configuration. The optical lithography microfabrication of the overlapping top gates is based on multiple layers of low-temperature atomic layer deposited hafnium oxide, which acts as a gate dielectric and as a robust insulating layer between two overlapping gate electrodes exhibiting a large dielectric breakdown field of . The advantage of overlapping gates over the split gate approach is confirmed in model calculations of the electrostatics of the gate stack. The overlapping gate process is applied to Hall bar devices of mercury telluride in order to study the interaction of different quantum Hall states in the nn′, np, pn and pp′ regime.
Spectral Asymmetry Induces a Re‐Entrant Quantum Hall Effect in a Topological Insulator. Wang, Li‐Xian; Beugeling, Wouter; Schmitt, Fabian; Lunczer, Lukas; Mayer, Julian‐Benedikt; Buhmann, Hartmut; Hankiewicz, Ewelina M.; Molenkamp, Laurens W. In Advanced Science. Wiley, 2024.
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The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

@article{Wang_2024, abstract = {The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.}, author = {Wang, Li‐Xian and Beugeling, Wouter and Schmitt, Fabian and Lunczer, Lukas and Mayer, Julian‐Benedikt and Buhmann, Hartmut and Hankiewicz, Ewelina M. and Molenkamp, Laurens W.}, journal = {Advanced Science}, keywords = {qt}, month = {03}, publisher = {Wiley}, title = {Spectral Asymmetry Induces a Re‐Entrant Quantum Hall Effect in a Topological Insulator}, year = 2024 }

%0 Journal Article %1 Wang_2024 %A Wang, Li‐Xian %A Beugeling, Wouter %A Schmitt, Fabian %A Lunczer, Lukas %A Mayer, Julian‐Benedikt %A Buhmann, Hartmut %A Hankiewicz, Ewelina M. %A Molenkamp, Laurens W. %D 2024 %I Wiley %J Advanced Science %R 10.1002/advs.202307447 %T Spectral Asymmetry Induces a Re‐Entrant Quantum Hall Effect in a Topological Insulator %U http://dx.doi.org/10.1002/advs.202307447 %X The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

Fast low bias pulsed DC transport measurements for the investigation of low temperature transport effects in semiconductor devices. Fuchs, C.; Hofer, M.; Fürst, L.; Shamim, S.; Kießling, T.; Buhmann, H.; Molenkamp, L. W. In Journal of Applied Physics, 134(17). AIP Publishing, 2023.
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We present a setup for fast, low-bias (< 1 mV) DC transport measurements with μs time resolution for high ohmic resistance (~ 20 kΩ) semiconducting samples.We discuss the circuitry and instrumentation for the measurement approach that can be applied to any kind of semiconductor device or (gated) two-dimensional material and demonstrate the main measurement artifacts in typical measurements by means of circuit simulation. Based on the latter, we present a simple two-step protocol for eliminating the measurement artifacts reliably. We demonstrate the technique by measuring the transitions between quantum Hall plateaus in the HgTe quantum wells and resolve plateaus as short-lived as 100 μs.

@article{Fuchs_2023, abstract = {We present a setup for fast, low-bias (< 1 mV) DC transport measurements with μs time resolution for high ohmic resistance ( 20 kΩ) semiconducting samples.We discuss the circuitry and instrumentation for the measurement approach that can be applied to any kind of semiconductor device or (gated) two-dimensional material and demonstrate the main measurement artifacts in typical measurements by means of circuit simulation. Based on the latter, we present a simple two-step protocol for eliminating the measurement artifacts reliably. We demonstrate the technique by measuring the transitions between quantum Hall plateaus in the HgTe quantum wells and resolve plateaus as short-lived as 100 μs.}, author = {Fuchs, C. and Hofer, M. and Fürst, L. and Shamim, S. and Kießling, T. and Buhmann, H. and Molenkamp, L. W.}, journal = {Journal of Applied Physics}, keywords = {qt}, month = 11, number = 17, publisher = {AIP Publishing}, title = {Fast low bias pulsed DC transport measurements for the investigation of low temperature transport effects in semiconductor devices}, volume = 134, year = 2023 }

%0 Journal Article %1 Fuchs_2023 %A Fuchs, C. %A Hofer, M. %A Fürst, L. %A Shamim, S. %A Kießling, T. %A Buhmann, H. %A Molenkamp, L. W. %D 2023 %I AIP Publishing %J Journal of Applied Physics %N 17 %R 10.1063/5.0170478 %T Fast low bias pulsed DC transport measurements for the investigation of low temperature transport effects in semiconductor devices %V 134 %X We present a setup for fast, low-bias (< 1 mV) DC transport measurements with μs time resolution for high ohmic resistance (~ 20 kΩ) semiconducting samples.We discuss the circuitry and instrumentation for the measurement approach that can be applied to any kind of semiconductor device or (gated) two-dimensional material and demonstrate the main measurement artifacts in typical measurements by means of circuit simulation. Based on the latter, we present a simple two-step protocol for eliminating the measurement artifacts reliably. We demonstrate the technique by measuring the transitions between quantum Hall plateaus in the HgTe quantum wells and resolve plateaus as short-lived as 100 μs.
Kondo interaction of quantum spin Hall edge channels with charge puddles. Fuchs, Christopher; Shamim, Saquib; Shekhar, Pragya; Fürst, Lena; Kleinlein, Johannes; Väyrynen, Jukka I.; Buhmann, Hartmut; Molenkamp, Laurens W. In Phys. Rev. B, 108(20), p. 205302. American Physical Society, 2023.
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Under time-reversal symmetry, quantum spin Hall edge channels are protected against elastic backscattering. However, even for samples which exhibit conductance quantization due to the quantum spin Hall effect, reproducible fluctuations shape the quantization plateau when the chemical potential is tuned through the bulk gap. Here, we examine those fluctuations in micron-sized HgTe quantum well devices. By performing temperature- and gate-dependent measurements, we conclude that “charge puddles” in the narrow-gap material have a Kondo-type interaction with the edge channels resulting in the observed conductance fluctuations. Our results provide insight into the underlying mechanisms of scattering in quantum spin Hall edge channels.

@article{PhysRevB.108.205302, abstract = {Under time-reversal symmetry, quantum spin Hall edge channels are protected against elastic backscattering. However, even for samples which exhibit conductance quantization due to the quantum spin Hall effect, reproducible fluctuations shape the quantization plateau when the chemical potential is tuned through the bulk gap. Here, we examine those fluctuations in micron-sized HgTe quantum well devices. By performing temperature- and gate-dependent measurements, we conclude that “charge puddles” in the narrow-gap material have a Kondo-type interaction with the edge channels resulting in the observed conductance fluctuations. Our results provide insight into the underlying mechanisms of scattering in quantum spin Hall edge channels.}, author = {Fuchs, Christopher and Shamim, Saquib and Shekhar, Pragya and Fürst, Lena and Kleinlein, Johannes and Väyrynen, Jukka I. and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 11, number = 20, pages = 205302, publisher = {American Physical Society}, title = {Kondo interaction of quantum spin Hall edge channels with charge puddles}, volume = 108, year = 2023 }

%0 Journal Article %1 PhysRevB.108.205302 %A Fuchs, Christopher %A Shamim, Saquib %A Shekhar, Pragya %A Fürst, Lena %A Kleinlein, Johannes %A Väyrynen, Jukka I. %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2023 %I American Physical Society %J Phys. Rev. B %N 20 %P 205302 %R 10.1103/PhysRevB.108.205302 %T Kondo interaction of quantum spin Hall edge channels with charge puddles %V 108 %X Under time-reversal symmetry, quantum spin Hall edge channels are protected against elastic backscattering. However, even for samples which exhibit conductance quantization due to the quantum spin Hall effect, reproducible fluctuations shape the quantization plateau when the chemical potential is tuned through the bulk gap. Here, we examine those fluctuations in micron-sized HgTe quantum well devices. By performing temperature- and gate-dependent measurements, we conclude that “charge puddles” in the narrow-gap material have a Kondo-type interaction with the edge channels resulting in the observed conductance fluctuations. Our results provide insight into the underlying mechanisms of scattering in quantum spin Hall edge channels.
Giant THz Nonlinearity in Topological and Trivial HgTe-Based Heterostructures. Uaman Svetikova, T. A.; de Oliveira, T. V. A. G.; Pashkin, A.; Ponomaryov, A.; Berger, C.; Fürst, L.; Bayer, F. B.; Novik, E. G.; Buhmann, H.; Molenkamp, L. W.; Helm, M.; Kiessling, T.; Winnerl, S.; Kovalev, S.; Astakhov, G. V. In ACS Photonics, 10(10), pp. 3708–3714. American Chemical Society (ACS), 2023.
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Nonlinear phenomena in the THz spectral domain are important for understanding the optoelectronic properties of quantum systems and provide a basis for modern information technologies. Here, we report a giant THz nonlinearity in high-mobility 2D topological insulators based on HgTe quantum wells, which manifests itself in a highly efficient third harmonic generation. We observe a third harmonic THz susceptibility several times higher than that in bare graphene and many orders of magnitude higher than that in trivial quantum well structures based on other materials. To explain the strong nonlinearity of HgTe-based heterostructures at the THz frequencies, we consider the acceleration of free carriers with a high mobility and variable dispersion. This acceleration model, for which the nonparabolicity of the band dispersion is key, in combination with independently measured scattering time and conductivity, is in good agreement with our experimental data in a wide temperature range for THz fields below the saturation. Our approach provides a route to material engineering for THz applications based on frequency conversion.

@article{Uaman_Svetikova_2023, abstract = {Nonlinear phenomena in the THz spectral domain are important for understanding the optoelectronic properties of quantum systems and provide a basis for modern information technologies. Here, we report a giant THz nonlinearity in high-mobility 2D topological insulators based on HgTe quantum wells, which manifests itself in a highly efficient third harmonic generation. We observe a third harmonic THz susceptibility several times higher than that in bare graphene and many orders of magnitude higher than that in trivial quantum well structures based on other materials. To explain the strong nonlinearity of HgTe-based heterostructures at the THz frequencies, we consider the acceleration of free carriers with a high mobility and variable dispersion. This acceleration model, for which the nonparabolicity of the band dispersion is key, in combination with independently measured scattering time and conductivity, is in good agreement with our experimental data in a wide temperature range for THz fields below the saturation. Our approach provides a route to material engineering for THz applications based on frequency conversion.}, author = {Uaman Svetikova, T. A. and de Oliveira, T. V. A. G. and Pashkin, A. and Ponomaryov, A. and Berger, C. and Fürst, L. and Bayer, F. B. and Novik, E. G. and Buhmann, H. and Molenkamp, L. W. and Helm, M. and Kiessling, T. and Winnerl, S. and Kovalev, S. and Astakhov, G. V.}, journal = {ACS Photonics}, keywords = {qt}, month = {09}, number = 10, pages = {3708–3714}, publisher = {American Chemical Society (ACS)}, title = {Giant THz Nonlinearity in Topological and Trivial HgTe-Based Heterostructures}, volume = 10, year = 2023 }

%0 Journal Article %1 Uaman_Svetikova_2023 %A Uaman Svetikova, T. A. %A de Oliveira, T. V. A. G. %A Pashkin, A. %A Ponomaryov, A. %A Berger, C. %A Fürst, L. %A Bayer, F. B. %A Novik, E. G. %A Buhmann, H. %A Molenkamp, L. W. %A Helm, M. %A Kiessling, T. %A Winnerl, S. %A Kovalev, S. %A Astakhov, G. V. %D 2023 %I American Chemical Society (ACS) %J ACS Photonics %N 10 %P 3708–3714 %R 10.1021/acsphotonics.3c00867 %T Giant THz Nonlinearity in Topological and Trivial HgTe-Based Heterostructures %V 10 %X Nonlinear phenomena in the THz spectral domain are important for understanding the optoelectronic properties of quantum systems and provide a basis for modern information technologies. Here, we report a giant THz nonlinearity in high-mobility 2D topological insulators based on HgTe quantum wells, which manifests itself in a highly efficient third harmonic generation. We observe a third harmonic THz susceptibility several times higher than that in bare graphene and many orders of magnitude higher than that in trivial quantum well structures based on other materials. To explain the strong nonlinearity of HgTe-based heterostructures at the THz frequencies, we consider the acceleration of free carriers with a high mobility and variable dispersion. This acceleration model, for which the nonparabolicity of the band dispersion is key, in combination with independently measured scattering time and conductivity, is in good agreement with our experimental data in a wide temperature range for THz fields below the saturation. Our approach provides a route to material engineering for THz applications based on frequency conversion.
Velocity and confinement of edge plasmons in HgTe-based two-dimensional topological insulators. Gourmelon, Alexandre; Frigerio, Elric; Kamata, Hiroshi; Lunczer, Lukas; Denis, Anne; Morfin, Pascal; Rosticher, Michael; Berroir, Jean-Marc; Fève, Gwendal; Placais, Bernard; Buhmann, Hartmut; Molenkamp, Laurens W.; Bocquillon, Erwann. In Phys. Rev. B, 108(3), p. 035405. American Physical Society, 2023.
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High-frequency transport in the edge states of the quantum spin Hall (QSH) effect has rarely been explored, though it could cast light on the scattering mechanisms taking place therein. Here we report on the measurement of the plasmon velocity in topological HgTe quantum wells both in the QSH and quantum Hall (QH) regimes, using harmonic GHz excitations and phase-resolved detection. We observe low plasmon velocities in both regimes, with, in particular, large transverse widths in the QH regime despite a sharp edge confinement profile. We ascribe these observations to the prominent influence of charge puddles forming in the vicinity of edge channels. Together with other recent works, it suggests that puddles play an essential role in the edge state physics and probably constitute a main hurdle on the way to clean and robust edge transport.

@article{PhysRevB.108.035405, abstract = {High-frequency transport in the edge states of the quantum spin Hall (QSH) effect has rarely been explored, though it could cast light on the scattering mechanisms taking place therein. Here we report on the measurement of the plasmon velocity in topological HgTe quantum wells both in the QSH and quantum Hall (QH) regimes, using harmonic GHz excitations and phase-resolved detection. We observe low plasmon velocities in both regimes, with, in particular, large transverse widths in the QH regime despite a sharp edge confinement profile. We ascribe these observations to the prominent influence of charge puddles forming in the vicinity of edge channels. Together with other recent works, it suggests that puddles play an essential role in the edge state physics and probably constitute a main hurdle on the way to clean and robust edge transport.}, author = {Gourmelon, Alexandre and Frigerio, Elric and Kamata, Hiroshi and Lunczer, Lukas and Denis, Anne and Morfin, Pascal and Rosticher, Michael and Berroir, Jean-Marc and Fève, Gwendal and Placais, Bernard and Buhmann, Hartmut and Molenkamp, Laurens W. and Bocquillon, Erwann}, journal = {Phys. Rev. B}, keywords = {qt}, month = {07}, number = 3, pages = {035405}, publisher = {American Physical Society}, title = {Velocity and confinement of edge plasmons in HgTe-based two-dimensional topological insulators}, volume = 108, year = 2023 }

%0 Journal Article %1 PhysRevB.108.035405 %A Gourmelon, Alexandre %A Frigerio, Elric %A Kamata, Hiroshi %A Lunczer, Lukas %A Denis, Anne %A Morfin, Pascal %A Rosticher, Michael %A Berroir, Jean-Marc %A Fève, Gwendal %A Placais, Bernard %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Bocquillon, Erwann %D 2023 %I American Physical Society %J Phys. Rev. B %N 3 %P 035405 %R 10.1103/PhysRevB.108.035405 %T Velocity and confinement of edge plasmons in HgTe-based two-dimensional topological insulators %V 108 %X High-frequency transport in the edge states of the quantum spin Hall (QSH) effect has rarely been explored, though it could cast light on the scattering mechanisms taking place therein. Here we report on the measurement of the plasmon velocity in topological HgTe quantum wells both in the QSH and quantum Hall (QH) regimes, using harmonic GHz excitations and phase-resolved detection. We observe low plasmon velocities in both regimes, with, in particular, large transverse widths in the QH regime despite a sharp edge confinement profile. We ascribe these observations to the prominent influence of charge puddles forming in the vicinity of edge channels. Together with other recent works, it suggests that puddles play an essential role in the edge state physics and probably constitute a main hurdle on the way to clean and robust edge transport.
Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials. Thenapparambil, Arya; dos Santos, Graciely Elias; Li, Chang-An; Abdelghany, Mohamed; Beugeling, Wouter; Buhmann, Hartmut; Gould, Charles; Zhang, Song-Bo; Trauzettel, Björn; Molenkamp, Laurens W. In Nano Letters, 23(15), pp. 6914–6919. American Chemical Society (ACS), 2023.
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Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.

@article{Thenapparambil_2023, abstract = {Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.}, author = {Thenapparambil, Arya and dos Santos, Graciely Elias and Li, Chang-An and Abdelghany, Mohamed and Beugeling, Wouter and Buhmann, Hartmut and Gould, Charles and Zhang, Song-Bo and Trauzettel, Björn and Molenkamp, Laurens W.}, journal = {Nano Letters}, keywords = {qt}, month = {07}, number = 15, pages = {6914–6919}, publisher = {American Chemical Society (ACS)}, title = {Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials}, volume = 23, year = 2023 }

%0 Journal Article %1 Thenapparambil_2023 %A Thenapparambil, Arya %A dos Santos, Graciely Elias %A Li, Chang-An %A Abdelghany, Mohamed %A Beugeling, Wouter %A Buhmann, Hartmut %A Gould, Charles %A Zhang, Song-Bo %A Trauzettel, Björn %A Molenkamp, Laurens W. %D 2023 %I American Chemical Society (ACS) %J Nano Letters %N 15 %P 6914–6919 %R 10.1021/acs.nanolett.3c01508 %T Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials %V 23 %X Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.
Realization of smooth side profile using diffusion-controlled wet chemical etching for HgTe/(Hg,Cd)Te heterostructures. Shekhar, Pragya; Bendias, Kalle; Fürst, Lena; Liang, Xianhu; Gbordzoe, Michael K; Borzenko, Tatiana; Buhmann, Hartmut; Kleinlein, Johannes; Molenkamp, Laurens W. In Nanotechnology, 34(20), p. 205302. IOP Publishing, 2023.
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We utilize a diffusion-controlled wet chemical etching technique to fabricate microstructures from two-dimensional HgTe/(Hg,Cd)Te-based topological insulators. For this purpose, we employ a KI: I2: HBr: H2O-based etchant. Investigation of the side profile of the etched heterostructure reveals that HgTe quantum wells protrude from the layer stack as a result of the different etch rates of the layers. This constraint poses challenges for the study of the transport properties of edge channels in HgTe quantum wells. In order to achieve a smoother side profile, we develop a novel approach to the etching process involving the incorporation of a sacrificial design element in the etch mask. This limits the flow of charge carriers to the ions in the electrolyte during the etching process. The simplicity of the method coupled with the promising results achieved thereby should make it possible for the new approach introduced here to be applied to other semiconductor heterostructures.

@article{Shekhar_2023, abstract = {We utilize a diffusion-controlled wet chemical etching technique to fabricate microstructures from two-dimensional HgTe/(Hg,Cd)Te-based topological insulators. For this purpose, we employ a KI: I2: HBr: H2O-based etchant. Investigation of the side profile of the etched heterostructure reveals that HgTe quantum wells protrude from the layer stack as a result of the different etch rates of the layers. This constraint poses challenges for the study of the transport properties of edge channels in HgTe quantum wells. In order to achieve a smoother side profile, we develop a novel approach to the etching process involving the incorporation of a sacrificial design element in the etch mask. This limits the flow of charge carriers to the ions in the electrolyte during the etching process. The simplicity of the method coupled with the promising results achieved thereby should make it possible for the new approach introduced here to be applied to other semiconductor heterostructures.}, author = {Shekhar, Pragya and Bendias, Kalle and Fürst, Lena and Liang, Xianhu and Gbordzoe, Michael K and Borzenko, Tatiana and Buhmann, Hartmut and Kleinlein, Johannes and Molenkamp, Laurens W}, journal = {Nanotechnology}, keywords = {qt}, month = {03}, number = 20, pages = 205302, publisher = {IOP Publishing}, title = {Realization of smooth side profile using diffusion-controlled wet chemical etching for HgTe/(Hg,Cd)Te heterostructures}, volume = 34, year = 2023 }

%0 Journal Article %1 Shekhar_2023 %A Shekhar, Pragya %A Bendias, Kalle %A Fürst, Lena %A Liang, Xianhu %A Gbordzoe, Michael K %A Borzenko, Tatiana %A Buhmann, Hartmut %A Kleinlein, Johannes %A Molenkamp, Laurens W %D 2023 %I IOP Publishing %J Nanotechnology %N 20 %P 205302 %R 10.1088/1361-6528/acba1d %T Realization of smooth side profile using diffusion-controlled wet chemical etching for HgTe/(Hg,Cd)Te heterostructures %V 34 %X We utilize a diffusion-controlled wet chemical etching technique to fabricate microstructures from two-dimensional HgTe/(Hg,Cd)Te-based topological insulators. For this purpose, we employ a KI: I2: HBr: H2O-based etchant. Investigation of the side profile of the etched heterostructure reveals that HgTe quantum wells protrude from the layer stack as a result of the different etch rates of the layers. This constraint poses challenges for the study of the transport properties of edge channels in HgTe quantum wells. In order to achieve a smoother side profile, we develop a novel approach to the etching process involving the incorporation of a sacrificial design element in the etch mask. This limits the flow of charge carriers to the ions in the electrolyte during the etching process. The simplicity of the method coupled with the promising results achieved thereby should make it possible for the new approach introduced here to be applied to other semiconductor heterostructures.
Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission. Vidal, Raphael C.; Marini, Giovanni; Lunczer, Lukas; Moser, Simon; Fürst, Lena; Issing, Julia; Jozwiak, Chris; Bostwick, Aaron; Rotenberg, Eli; Gould, Charles; Buhmann, Hartmut; Beugeling, Wouter; Sangiovanni, Giorgio; Di Sante, Domenico; Profeta, Gianni; Molenkamp, Laurens W.; Bentmann, Hendrik; Reinert, Friedrich. In Phys. Rev. B, 107(12), p. L121102. American Physical Society, 2023.
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HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy.We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.

@article{PhysRevB.107.L121102, abstract = {HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy.We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.}, author = {Vidal, Raphael C. and Marini, Giovanni and Lunczer, Lukas and Moser, Simon and Fürst, Lena and Issing, Julia and Jozwiak, Chris and Bostwick, Aaron and Rotenberg, Eli and Gould, Charles and Buhmann, Hartmut and Beugeling, Wouter and Sangiovanni, Giorgio and Di Sante, Domenico and Profeta, Gianni and Molenkamp, Laurens W. and Bentmann, Hendrik and Reinert, Friedrich}, journal = {Phys. Rev. B}, keywords = {qt}, month = {03}, number = 12, pages = {L121102}, publisher = {American Physical Society}, title = {Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission}, volume = 107, year = 2023 }

%0 Journal Article %1 PhysRevB.107.L121102 %A Vidal, Raphael C. %A Marini, Giovanni %A Lunczer, Lukas %A Moser, Simon %A Fürst, Lena %A Issing, Julia %A Jozwiak, Chris %A Bostwick, Aaron %A Rotenberg, Eli %A Gould, Charles %A Buhmann, Hartmut %A Beugeling, Wouter %A Sangiovanni, Giorgio %A Di Sante, Domenico %A Profeta, Gianni %A Molenkamp, Laurens W. %A Bentmann, Hendrik %A Reinert, Friedrich %D 2023 %I American Physical Society %J Phys. Rev. B %N 12 %P L121102 %R 10.1103/PhysRevB.107.L121102 %T Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission %U https://link.aps.org/doi/10.1103/PhysRevB.107.L121102 %V 107 %X HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy.We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.

Low-Temperature Atomic Layer Deposition of Hafnium Oxide for Gating Applications. Shekhar, Pragya; Shamim, Saquib; Hartinger, Simon; Schlereth, Raimund; Hock, Volkmar; Buhmann, Hartmut; Kleinlein, Johannes; Molenkamp, Laurens W. In {ACS} Applied Materials {\&}amp$\mathsemicolon$ Interfaces, 14(29), pp. 33960–33967. American Chemical Society ({ACS}), 2022.
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We present a novel low-temperature (30 °C) atomic layer deposition process for hafnium oxide and apply the layers as gate dielectric to fabricate devices out of the thermally sensitive topological insulator HgTe. The key to achieving selflimiting growth at these low temperatures is the incorporation of sufficiently long purge times ( ≥150 s) in the deposition cycles. We investigate the structural and compositional properties of these thin films using X-ray reflectometry and photoelectron spectroscopy, finding a growth rate of 1.6 Å per cycle and an atomic ratio of Hf/O of 1:1.85. In addition, we report on the transport properties of the microstructured devices, which are much enhanced compared to previous device generations. We determine a relative permittivity of ∼15 for our HfO2 layers. Our process considerably reduces the thermal load of the samples during microfabrication and can be adapted to a broad range of materials, enabling the fabrication of high-quality gate insulators on various temperaturesensitive materials.

@article{Shekhar_2022, abstract = {We present a novel low-temperature (30 °C) atomic layer deposition process for hafnium oxide and apply the layers as gate dielectric to fabricate devices out of the thermally sensitive topological insulator HgTe. The key to achieving selflimiting growth at these low temperatures is the incorporation of sufficiently long purge times ( ≥150 s) in the deposition cycles. We investigate the structural and compositional properties of these thin films using X-ray reflectometry and photoelectron spectroscopy, finding a growth rate of 1.6 Å per cycle and an atomic ratio of Hf/O of 1:1.85. In addition, we report on the transport properties of the microstructured devices, which are much enhanced compared to previous device generations. We determine a relative permittivity of ∼15 for our HfO2 layers. Our process considerably reduces the thermal load of the samples during microfabrication and can be adapted to a broad range of materials, enabling the fabrication of high-quality gate insulators on various temperaturesensitive materials.}, author = {Shekhar, Pragya and Shamim, Saquib and Hartinger, Simon and Schlereth, Raimund and Hock, Volkmar and Buhmann, Hartmut and Kleinlein, Johannes and Molenkamp, Laurens W.}, journal = {{ACS} Applied Materials {\&}amp$\mathsemicolon$ Interfaces}, keywords = {qt}, month = {07}, number = 29, pages = {33960–33967}, publisher = {American Chemical Society ({ACS})}, title = {Low-Temperature Atomic Layer Deposition of Hafnium Oxide for Gating Applications}, volume = 14, year = 2022 }

%0 Journal Article %1 Shekhar_2022 %A Shekhar, Pragya %A Shamim, Saquib %A Hartinger, Simon %A Schlereth, Raimund %A Hock, Volkmar %A Buhmann, Hartmut %A Kleinlein, Johannes %A Molenkamp, Laurens W. %D 2022 %I American Chemical Society ({ACS}) %J {ACS} Applied Materials {\&}amp$\mathsemicolon$ Interfaces %N 29 %P 33960--33967 %R 10.1021/acsami.2c06176 %T Low-Temperature Atomic Layer Deposition of Hafnium Oxide for Gating Applications %V 14 %X We present a novel low-temperature (30 °C) atomic layer deposition process for hafnium oxide and apply the layers as gate dielectric to fabricate devices out of the thermally sensitive topological insulator HgTe. The key to achieving selflimiting growth at these low temperatures is the incorporation of sufficiently long purge times ( ≥150 s) in the deposition cycles. We investigate the structural and compositional properties of these thin films using X-ray reflectometry and photoelectron spectroscopy, finding a growth rate of 1.6 Å per cycle and an atomic ratio of Hf/O of 1:1.85. In addition, we report on the transport properties of the microstructured devices, which are much enhanced compared to previous device generations. We determine a relative permittivity of ∼15 for our HfO2 layers. Our process considerably reduces the thermal load of the samples during microfabrication and can be adapted to a broad range of materials, enabling the fabrication of high-quality gate insulators on various temperaturesensitive materials.
Counterpropagating topological and quantum Hall edge channels. Shamim, Saquib; Shekhar, Pragya; Beugeling, Wouter; Böttcher, Jan; Budewitz, Andreas; Mayer, Julian-Benedikt; Lunczer, Lukas; Hankiewicz, Ewelina M.; Buhmann, Hartmut; Molenkamp, Laurens W. In Nature Communications, 13(1). Springer Science and Business Media {LLC}, 2022.
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The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to h/e2. By tuning the disorder using different fabrication processes, we find evidence that this unexpected ν = 1 plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.

@article{Shamim_2022, abstract = {The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to h/e2. By tuning the disorder using different fabrication processes, we find evidence that this unexpected ν = 1 plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.}, author = {Shamim, Saquib and Shekhar, Pragya and Beugeling, Wouter and Böttcher, Jan and Budewitz, Andreas and Mayer, Julian-Benedikt and Lunczer, Lukas and Hankiewicz, Ewelina M. and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nature Communications}, keywords = {qt}, month = {05}, number = 1, publisher = {Springer Science and Business Media {LLC}}, title = {Counterpropagating topological and quantum Hall edge channels}, volume = 13, year = 2022 }

%0 Journal Article %1 Shamim_2022 %A Shamim, Saquib %A Shekhar, Pragya %A Beugeling, Wouter %A Böttcher, Jan %A Budewitz, Andreas %A Mayer, Julian-Benedikt %A Lunczer, Lukas %A Hankiewicz, Ewelina M. %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2022 %I Springer Science and Business Media {LLC} %J Nature Communications %N 1 %R 10.1038/s41467-022-29815-2 %T Counterpropagating topological and quantum Hall edge channels %U https://doi.org/10.1038%2Fs41467-022-29815-2 %V 13 %X The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to h/e2. By tuning the disorder using different fabrication processes, we find evidence that this unexpected ν = 1 plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.

Massive and Topological Surface States in Tensile-Strained {HgTe}. Mahler, David M.; Müller, Valentin L.; Thienel, Cornelius; Wiedenmann, Jonas; Beugeling, Wouter; Buhmann, Hartmut; Molenkamp, Laurens W. In Nano Letters, 21(23), pp. 9869–9874. American Chemical Society ({ACS}), 2021.
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Magneto-transport measurements on gated highmobility heterostructures containing a 60 nm layer of tensile-strained HgTe, a three-dimensional topological insulator, show well-developed Hall quantization from surface states both in the n- as well as in the ptype regime. While the n-type behavior is due to transport in the topological surface state of the material, we find from 8-orbital k·p calculations that the p-type transport results from massive Volkov−Pankratov states. Their formation prevents the Dirac point and thus the p-conducting topological surface state from being accessible in transport experiments. This interpretation is supported by low-field magneto-transport experiments demonstrating the coexistence of nconducting topological surface states and p-conducting Volkov−Pankratov states at the relevant gate voltages.

@article{Mahler_2021, abstract = {Magneto-transport measurements on gated highmobility heterostructures containing a 60 nm layer of tensile-strained HgTe, a three-dimensional topological insulator, show well-developed Hall quantization from surface states both in the n- as well as in the ptype regime. While the n-type behavior is due to transport in the topological surface state of the material, we find from 8-orbital k·p calculations that the p-type transport results from massive Volkov−Pankratov states. Their formation prevents the Dirac point and thus the p-conducting topological surface state from being accessible in transport experiments. This interpretation is supported by low-field magneto-transport experiments demonstrating the coexistence of nconducting topological surface states and p-conducting Volkov−Pankratov states at the relevant gate voltages.}, author = {Mahler, David M. and Müller, Valentin L. and Thienel, Cornelius and Wiedenmann, Jonas and Beugeling, Wouter and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nano Letters}, keywords = {qt}, month = 11, number = 23, pages = {9869–9874}, publisher = {American Chemical Society ({ACS})}, title = {Massive and Topological Surface States in Tensile-Strained {HgTe}}, volume = 21, year = 2021 }

%0 Journal Article %1 Mahler_2021 %A Mahler, David M. %A Müller, Valentin L. %A Thienel, Cornelius %A Wiedenmann, Jonas %A Beugeling, Wouter %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2021 %I American Chemical Society ({ACS}) %J Nano Letters %N 23 %P 9869--9874 %R 10.1021/acs.nanolett.1c02456 %T Massive and Topological Surface States in Tensile-Strained {HgTe} %U https://doi.org/10.1021%2Facs.nanolett.1c02456 %V 21 %X Magneto-transport measurements on gated highmobility heterostructures containing a 60 nm layer of tensile-strained HgTe, a three-dimensional topological insulator, show well-developed Hall quantization from surface states both in the n- as well as in the ptype regime. While the n-type behavior is due to transport in the topological surface state of the material, we find from 8-orbital k·p calculations that the p-type transport results from massive Volkov−Pankratov states. Their formation prevents the Dirac point and thus the p-conducting topological surface state from being accessible in transport experiments. This interpretation is supported by low-field magneto-transport experiments demonstrating the coexistence of nconducting topological surface states and p-conducting Volkov−Pankratov states at the relevant gate voltages.
Electron{\textendash}Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator. Müller, Valentin L.; Yan, Yuan; Kashuba, Oleksiy; Trauzettel, Björn; Abdelghany, Mohamed; Kleinlein, Johannes; Beugeling, Wouter; Buhmann, Hartmut; Molenkamp, Laurens W. In Nano Letters. American Chemical Society ({ACS}), 2021.
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We have experimentally investigated the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We have found that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a nonmonotonic differential resistance of narrow channels. We have shown that the observed initial increase in resistance can be attributed to electron−hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron−hole scattering in the transport properties of topological insulators.

@article{M_ller_2021, abstract = {We have experimentally investigated the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We have found that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a nonmonotonic differential resistance of narrow channels. We have shown that the observed initial increase in resistance can be attributed to electron−hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron−hole scattering in the transport properties of topological insulators.}, author = {Müller, Valentin L. and Yan, Yuan and Kashuba, Oleksiy and Trauzettel, Björn and Abdelghany, Mohamed and Kleinlein, Johannes and Beugeling, Wouter and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nano Letters}, keywords = {qt}, month = {06}, publisher = {American Chemical Society ({ACS})}, title = {Electron{\textendash}Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator}, year = 2021 }

%0 Journal Article %1 M_ller_2021 %A Müller, Valentin L. %A Yan, Yuan %A Kashuba, Oleksiy %A Trauzettel, Björn %A Abdelghany, Mohamed %A Kleinlein, Johannes %A Beugeling, Wouter %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2021 %I American Chemical Society ({ACS}) %J Nano Letters %R 10.1021/acs.nanolett.1c01271 %T Electron{\textendash}Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator %U https://doi.org/10.1021%2Facs.nanolett.1c01271 %X We have experimentally investigated the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We have found that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a nonmonotonic differential resistance of narrow channels. We have shown that the observed initial increase in resistance can be attributed to electron−hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron−hole scattering in the transport properties of topological insulators.

Selective area grown ZnTe nanowires as the basis for quasi-one-dimensional CdTe-HgTe multishell heterostructures. Hajer, J.; Mantei, W.; Kessel, M.; Brüne, C.; Wenner, S.; van Helvoort, A. T. J.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Materials, 4(6), p. 066001. American Physical Society, 2020.
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Selective area growth is employed in the vapor-liquid-solid molecular beam epitaxy of ZnTe nanowire arrays. Full control over the location of the individual nanowires is achieved by defined positioning of the growth catalyst. This study addresses the influence of substrate material and growth temperature on the yield of vertical nanowires. The optimized procedure provides arrays of single-crystalline free-standing nanowires with a high ensemble uniformity. The nanowires exhibit a uniform shape with a diameter of about 80 nm and reach a length of more than 3μm, which makes them suitable as substrates for core-shell nanowires of the topological insulator material HgTe.

@article{PhysRevMaterials.4.066001, abstract = {Selective area growth is employed in the vapor-liquid-solid molecular beam epitaxy of ZnTe nanowire arrays. Full control over the location of the individual nanowires is achieved by defined positioning of the growth catalyst. This study addresses the influence of substrate material and growth temperature on the yield of vertical nanowires. The optimized procedure provides arrays of single-crystalline free-standing nanowires with a high ensemble uniformity. The nanowires exhibit a uniform shape with a diameter of about 80 nm and reach a length of more than 3μm, which makes them suitable as substrates for core-shell nanowires of the topological insulator material HgTe.}, author = {Hajer, J. and Mantei, W. and Kessel, M. and Br\"une, C. and Wenner, S. and van Helvoort, A. T. J. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. Materials}, keywords = {qt}, month = {06}, number = 6, pages = {066001}, publisher = {American Physical Society}, title = {Selective area grown ZnTe nanowires as the basis for quasi-one-dimensional CdTe-HgTe multishell heterostructures}, volume = 4, year = 2020 }

%0 Journal Article %1 PhysRevMaterials.4.066001 %A Hajer, J. %A Mantei, W. %A Kessel, M. %A Brüne, C. %A Wenner, S. %A van Helvoort, A. T. J. %A Buhmann, H. %A Molenkamp, L. W. %D 2020 %I American Physical Society %J Phys. Rev. Materials %N 6 %P 066001 %R 10.1103/PhysRevMaterials.4.066001 %T Selective area grown ZnTe nanowires as the basis for quasi-one-dimensional CdTe-HgTe multishell heterostructures %V 4 %X Selective area growth is employed in the vapor-liquid-solid molecular beam epitaxy of ZnTe nanowire arrays. Full control over the location of the individual nanowires is achieved by defined positioning of the growth catalyst. This study addresses the influence of substrate material and growth temperature on the yield of vertical nanowires. The optimized procedure provides arrays of single-crystalline free-standing nanowires with a high ensemble uniformity. The nanowires exhibit a uniform shape with a diameter of about 80 nm and reach a length of more than 3μm, which makes them suitable as substrates for core-shell nanowires of the topological insulator material HgTe.
Band edge thermometry for the {MBE} growth of (Hg,Cd)Te-based materials. Schlereth, R.; Hajer, J.; Fürst, L.; Schreyeck, S.; Buhmann, H.; Molenkamp, L.W. In Journal of Crystal Growth, 537, p. 125602. Elsevier {BV}, 2020.
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The material system (Hg,Cd)Te is a prototype system for topological insulators and Dirac semi-metals. Molecular beam epitaxy is the preferred method for the growth of (Hg,Cd)Te epilayer heterostructures and CdTe-HgTe core-shell nanowires. Unfortunately, the high crystalline quality desired for charge transport investigations is only achieved for a very narrow window of the growth temperature. Additionally, the low growth temperature requires a special thermometry. Here, we demonstrate the improvement of the growth of (Hg,Cd)Te epilayer heterostructures and CdTe nanowires by the use of band edge thermometry. We show that even for narrow-gap materials band edge thermometry provides a suitable method to control the temperature directly at the growth front with a high precision and reproducibility, in contrast to a conventionally used thermocouple.

@article{Schlereth_2020, abstract = {The material system (Hg,Cd)Te is a prototype system for topological insulators and Dirac semi-metals. Molecular beam epitaxy is the preferred method for the growth of (Hg,Cd)Te epilayer heterostructures and CdTe-HgTe core-shell nanowires. Unfortunately, the high crystalline quality desired for charge transport investigations is only achieved for a very narrow window of the growth temperature. Additionally, the low growth temperature requires a special thermometry. Here, we demonstrate the improvement of the growth of (Hg,Cd)Te epilayer heterostructures and CdTe nanowires by the use of band edge thermometry. We show that even for narrow-gap materials band edge thermometry provides a suitable method to control the temperature directly at the growth front with a high precision and reproducibility, in contrast to a conventionally used thermocouple.}, author = {Schlereth, R. and Hajer, J. and Fürst, L. and Schreyeck, S. and Buhmann, H. and Molenkamp, L.W.}, journal = {Journal of Crystal Growth}, keywords = {qt}, month = {05}, pages = 125602, publisher = {Elsevier {BV}}, title = {Band edge thermometry for the {MBE} growth of (Hg,Cd)Te-based materials}, volume = 537, year = 2020 }

%0 Journal Article %1 Schlereth_2020 %A Schlereth, R. %A Hajer, J. %A Fürst, L. %A Schreyeck, S. %A Buhmann, H. %A Molenkamp, L.W. %D 2020 %I Elsevier {BV} %J Journal of Crystal Growth %P 125602 %R 10.1016/j.jcrysgro.2020.125602 %T Band edge thermometry for the {MBE} growth of (Hg,Cd)Te-based materials %V 537 %X The material system (Hg,Cd)Te is a prototype system for topological insulators and Dirac semi-metals. Molecular beam epitaxy is the preferred method for the growth of (Hg,Cd)Te epilayer heterostructures and CdTe-HgTe core-shell nanowires. Unfortunately, the high crystalline quality desired for charge transport investigations is only achieved for a very narrow window of the growth temperature. Additionally, the low growth temperature requires a special thermometry. Here, we demonstrate the improvement of the growth of (Hg,Cd)Te epilayer heterostructures and CdTe nanowires by the use of band edge thermometry. We show that even for narrow-gap materials band edge thermometry provides a suitable method to control the temperature directly at the growth front with a high precision and reproducibility, in contrast to a conventionally used thermocouple.
Dynamical Separation of Bulk and Edge Transport in HgTe-Based 2D Topological Insulators. Dartiailh, Matthieu C.; Hartinger, Simon; Gourmelon, Alexandre; Bendias, Kalle; Bartolomei, Hugo; Kamata, Hiroshi; Berroir, Jean-Marc; Fève, Gwendal; Pla\ifmmode \mboxç\else \c{c}\fi{}ais, Bernard; Lunczer, Lukas; Schlereth, Raimund; Buhmann, Hartmut; Molenkamp, Laurens W.; Bocquillon, Erwann. In Phys. Rev. Lett., 124(7), p. 076802. American Physical Society, 2020.
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Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with respect to bulk carriers. Our work on microwave spectroscopy highlights the response of the edges which host very mobile carriers, while bulk carriers are drastically slowed down in the gap. Though the edges are denser than expected, we establish that charge relaxation occurs on short timescales and suggest that edge states can be addressed selectively on timescales over which bulk carriers are frozen.

@article{PhysRevLett.124.076802, abstract = {Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with respect to bulk carriers. Our work on microwave spectroscopy highlights the response of the edges which host very mobile carriers, while bulk carriers are drastically slowed down in the gap. Though the edges are denser than expected, we establish that charge relaxation occurs on short timescales and suggest that edge states can be addressed selectively on timescales over which bulk carriers are frozen.}, author = {Dartiailh, Matthieu C. and Hartinger, Simon and Gourmelon, Alexandre and Bendias, Kalle and Bartolomei, Hugo and Kamata, Hiroshi and Berroir, Jean-Marc and F\`eve, Gwendal and Pla\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ais, Bernard and Lunczer, Lukas and Schlereth, Raimund and Buhmann, Hartmut and Molenkamp, Laurens W. and Bocquillon, Erwann}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {02}, number = 7, pages = {076802}, publisher = {American Physical Society}, title = {Dynamical Separation of Bulk and Edge Transport in HgTe-Based 2D Topological Insulators}, volume = 124, year = 2020 }

%0 Journal Article %1 PhysRevLett.124.076802 %A Dartiailh, Matthieu C. %A Hartinger, Simon %A Gourmelon, Alexandre %A Bendias, Kalle %A Bartolomei, Hugo %A Kamata, Hiroshi %A Berroir, Jean-Marc %A Fève, Gwendal %A Pla\ifmmode \mboxç\else \c{c}\fi{}ais, Bernard %A Lunczer, Lukas %A Schlereth, Raimund %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Bocquillon, Erwann %D 2020 %I American Physical Society %J Phys. Rev. Lett. %N 7 %P 076802 %R 10.1103/PhysRevLett.124.076802 %T Dynamical Separation of Bulk and Edge Transport in HgTe-Based 2D Topological Insulators %V 124 %X Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with respect to bulk carriers. Our work on microwave spectroscopy highlights the response of the edges which host very mobile carriers, while bulk carriers are drastically slowed down in the gap. Though the edges are denser than expected, we establish that charge relaxation occurs on short timescales and suggest that edge states can be addressed selectively on timescales over which bulk carriers are frozen.
Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator. Shamim, S.; Beugeling, W.; Böttcher, J.; Shekhar, P.; Budewitz, A.; Leubner, P.; Lunczer, L.; Hankiewicz, E.M.; Buhmann, H.; Molenkamp, L.W. In Science Advances, 6(26), p. eaba4625. 2020.
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The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.

@article{shamim2020emergent, abstract = {The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of 50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.}, author = {Shamim, S. and Beugeling, W. and Böttcher, J. and Shekhar, P. and Budewitz, A. and Leubner, P. and Lunczer, L. and Hankiewicz, E.M. and Buhmann, H. and Molenkamp, L.W.}, journal = {Science Advances}, keywords = {qt}, number = 26, pages = {eaba4625}, title = {Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator}, volume = 6, year = 2020 }

%0 Journal Article %1 shamim2020emergent %A Shamim, S. %A Beugeling, W. %A Böttcher, J. %A Shekhar, P. %A Budewitz, A. %A Leubner, P. %A Lunczer, L. %A Hankiewicz, E.M. %A Buhmann, H. %A Molenkamp, L.W. %D 2020 %J Science Advances %N 26 %P eaba4625 %R 10.1126/sciadv.aba4625 %T Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator %V 6 %X The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.

How to measure the entropy of a mesoscopic system via thermoelectric transport. Kleeorin, Yaakov; Thierschmann, Holger; Buhmann, Hartmut; Georges, Antoine; Molenkamp, Laurens W.; Meir, Yigal. In Nature Communications, 10(1). Springer Science and Business Media {LLC}, 2019.
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Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.

@article{Kleeorin_2019, abstract = {Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.}, author = {Kleeorin, Yaakov and Thierschmann, Holger and Buhmann, Hartmut and Georges, Antoine and Molenkamp, Laurens W. and Meir, Yigal}, journal = {Nature Communications}, keywords = {qt}, month = 12, number = 1, publisher = {Springer Science and Business Media {LLC}}, title = {How to measure the entropy of a mesoscopic system via thermoelectric transport}, volume = 10, year = 2019 }

%0 Journal Article %1 Kleeorin_2019 %A Kleeorin, Yaakov %A Thierschmann, Holger %A Buhmann, Hartmut %A Georges, Antoine %A Molenkamp, Laurens W. %A Meir, Yigal %D 2019 %I Springer Science and Business Media {LLC} %J Nature Communications %N 1 %R 10.1038/s41467-019-13630-3 %T How to measure the entropy of a mesoscopic system via thermoelectric transport %V 10 %X Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.
Interacting topological edge channels. Strunz, Jonas; Wiedenmann, Jonas; Fleckenstein, Christoph; Lunczer, Lukas; Beugeling, Wouter; Müller, Valentin L.; Shekhar, Pragya; Ziani, Niccol{{ò}} Traverso; Shamim, Saquib; Kleinlein, Johannes; Buhmann, Hartmut; Trauzettel, Björn; Molenkamp, Laurens W. In Nature Physics. Springer Science and Business Media {LLC}, 2019.
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Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical character of those states is by now well established experimentally, it is a fundamental open question how those edge states interact with each other when brought in spatial proximity. We employ a topological quantum point contact to guide edge channels from opposite sides into a quasi-one-dimensional constriction, based on inverted HgTe quantum wells. Apart from the expected quantization in integer steps of $2 e^2/h$, we find a surprising additional plateau at $e^2/h$. We explain our observation by combining band structure calculations and repulsive electron-electron interaction effects captured within the Tomonaga-Luttinger liquid model. The present results may have direct implications for the study of one-dimensional helical electron quantum optics, Majorana- and potentially para-fermions.

@article{Strunz_2019, abstract = {Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical character of those states is by now well established experimentally, it is a fundamental open question how those edge states interact with each other when brought in spatial proximity. We employ a topological quantum point contact to guide edge channels from opposite sides into a quasi-one-dimensional constriction, based on inverted HgTe quantum wells. Apart from the expected quantization in integer steps of $2 e^2/h$, we find a surprising additional plateau at $e^2/h$. We explain our observation by combining band structure calculations and repulsive electron-electron interaction effects captured within the Tomonaga-Luttinger liquid model. The present results may have direct implications for the study of one-dimensional helical electron quantum optics, Majorana- and potentially para-fermions.}, author = {Strunz, Jonas and Wiedenmann, Jonas and Fleckenstein, Christoph and Lunczer, Lukas and Beugeling, Wouter and Müller, Valentin L. and Shekhar, Pragya and Ziani, Niccol{\`{o}} Traverso and Shamim, Saquib and Kleinlein, Johannes and Buhmann, Hartmut and Trauzettel, Björn and Molenkamp, Laurens W.}, journal = {Nature Physics}, keywords = {qt}, month = 10, publisher = {Springer Science and Business Media {LLC}}, title = {Interacting topological edge channels}, year = 2019 }

%0 Journal Article %1 Strunz_2019 %A Strunz, Jonas %A Wiedenmann, Jonas %A Fleckenstein, Christoph %A Lunczer, Lukas %A Beugeling, Wouter %A Müller, Valentin L. %A Shekhar, Pragya %A Ziani, Niccol{{ò}} Traverso %A Shamim, Saquib %A Kleinlein, Johannes %A Buhmann, Hartmut %A Trauzettel, Björn %A Molenkamp, Laurens W. %D 2019 %I Springer Science and Business Media {LLC} %J Nature Physics %R 10.1038/s41567-019-0692-4 %T Interacting topological edge channels %X Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical character of those states is by now well established experimentally, it is a fundamental open question how those edge states interact with each other when brought in spatial proximity. We employ a topological quantum point contact to guide edge channels from opposite sides into a quasi-one-dimensional constriction, based on inverted HgTe quantum wells. Apart from the expected quantization in integer steps of $2 e^2/h$, we find a surprising additional plateau at $e^2/h$. We explain our observation by combining band structure calculations and repulsive electron-electron interaction effects captured within the Tomonaga-Luttinger liquid model. The present results may have direct implications for the study of one-dimensional helical electron quantum optics, Majorana- and potentially para-fermions.
Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe. Mahler, David M.; Mayer, Julian-Benedikt; Leubner, Philipp; Lunczer, Lukas; Di Sante, Domenico; Sangiovanni, Giorgio; Thomale, Ronny; Hankiewicz, Ewelina M.; Buhmann, Hartmut; Gould, Charles; Molenkamp, Laurens W. In Phys. Rev. X, 9(3), p. 031034. American Physical Society, 2019.
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Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Because of the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.

@article{PhysRevX.9.031034, abstract = {Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Because of the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.}, author = {Mahler, David M. and Mayer, Julian-Benedikt and Leubner, Philipp and Lunczer, Lukas and Di Sante, Domenico and Sangiovanni, Giorgio and Thomale, Ronny and Hankiewicz, Ewelina M. and Buhmann, Hartmut and Gould, Charles and Molenkamp, Laurens W.}, journal = {Phys. Rev. X}, keywords = {qt}, month = {08}, number = 3, pages = {031034}, publisher = {American Physical Society}, title = {Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe}, volume = 9, year = 2019 }

%0 Journal Article %1 PhysRevX.9.031034 %A Mahler, David M. %A Mayer, Julian-Benedikt %A Leubner, Philipp %A Lunczer, Lukas %A Di Sante, Domenico %A Sangiovanni, Giorgio %A Thomale, Ronny %A Hankiewicz, Ewelina M. %A Buhmann, Hartmut %A Gould, Charles %A Molenkamp, Laurens W. %D 2019 %I American Physical Society %J Phys. Rev. X %N 3 %P 031034 %R 10.1103/PhysRevX.9.031034 %T Interplay of Dirac Nodes and Volkov-Pankratov Surface States in Compressively Strained HgTe %V 9 %X Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Because of the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.
Proximity-Induced Superconductivity in {CdTe}{\textendash}{HgTe} Core{\textendash}Shell Nanowires. Hajer, Jan; Kessel, Maximilian; Brüne, Christoph; Stehno, Martin P.; Buhmann, Hartmut; Molenkamp, Laurens W. In Nano Letters, 19(6), pp. 4078–4082. American Chemical Society ({ACS}), 2019.
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In this Letter we report on proximity superconductivity induced in CdTe–HgTe core–shell nanowires, a quasi-one-dimensional heterostructure of the topological insulator HgTe. We demonstrate a Josephson supercurrent in our nanowires contacted with superconducting Al leads. The observation of a sizable IcRn product, a positive excess current, and multiple Andreev reflections up to fourth order further indicate a high interface quality of the junctions.

@article{hajer2019proximityinduced, abstract = {In this Letter we report on proximity superconductivity induced in CdTe–HgTe core–shell nanowires, a quasi-one-dimensional heterostructure of the topological insulator HgTe. We demonstrate a Josephson supercurrent in our nanowires contacted with superconducting Al leads. The observation of a sizable IcRn product, a positive excess current, and multiple Andreev reflections up to fourth order further indicate a high interface quality of the junctions.}, author = {Hajer, Jan and Kessel, Maximilian and Brüne, Christoph and Stehno, Martin P. and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nano Letters}, keywords = {qt}, month = {05}, number = 6, pages = {4078–4082}, publisher = {American Chemical Society ({ACS})}, title = {Proximity-Induced Superconductivity in {CdTe}{\textendash}{HgTe} Core{\textendash}Shell Nanowires}, volume = 19, year = 2019 }

%0 Journal Article %1 hajer2019proximityinduced %A Hajer, Jan %A Kessel, Maximilian %A Brüne, Christoph %A Stehno, Martin P. %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2019 %I American Chemical Society ({ACS}) %J Nano Letters %N 6 %P 4078--4082 %R 10.1021/acs.nanolett.9b01472 %T Proximity-Induced Superconductivity in {CdTe}{\textendash}{HgTe} Core{\textendash}Shell Nanowires %V 19 %X In this Letter we report on proximity superconductivity induced in CdTe–HgTe core–shell nanowires, a quasi-one-dimensional heterostructure of the topological insulator HgTe. We demonstrate a Josephson supercurrent in our nanowires contacted with superconducting Al leads. The observation of a sizable IcRn product, a positive excess current, and multiple Andreev reflections up to fourth order further indicate a high interface quality of the junctions.
Residual strain in free-standing CdTe nanowires overgrown with HgTe. Kessel, Maximilian; Lunczer, Lukas; Tarakina, Nadezda V.; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W. In Appl. Phys. Lett., 114(15), p. 153104-. American Institute of Physics, 2019.
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We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy and scanning transmission electron microscopy confirm that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use high-resolution X-ray diffraction to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in the lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain pattern with signatures of both uniaxial and shear strains present in the overgrown nanowires.

@article{kessel2019residual, abstract = {We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy and scanning transmission electron microscopy confirm that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use high-resolution X-ray diffraction to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in the lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain pattern with signatures of both uniaxial and shear strains present in the overgrown nanowires.}, author = {Kessel, Maximilian and Lunczer, Lukas and Tarakina, Nadezda V. and Brüne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {04}, number = 15, pages = {153104–}, publisher = {American Institute of Physics}, title = {Residual strain in free-standing CdTe nanowires overgrown with HgTe}, volume = 114, year = 2019 }

%0 Journal Article %1 kessel2019residual %A Kessel, Maximilian %A Lunczer, Lukas %A Tarakina, Nadezda V. %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %B Applied Physics Letters %D 2019 %I American Institute of Physics %J Appl. Phys. Lett. %N 15 %P 153104-- %R 10.1063/1.5085174 %T Residual strain in free-standing CdTe nanowires overgrown with HgTe %V 114 %X We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy and scanning transmission electron microscopy confirm that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use high-resolution X-ray diffraction to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in the lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain pattern with signatures of both uniaxial and shear strains present in the overgrown nanowires.
Magnetoresistance in the in-plane magnetic field induced semimetallic phase of inverted HgTe quantum wells. Khouri, T.; Pezzini, S.; Bendias, M.; Leubner, P.; Zeitler, U.; Hussey, N. E.; Buhmann, H.; Molenkamp, L. W.; Titov, M.; Wiedmann, S. In Phys. Rev. B, 99(7), p. 075303. American Physical Society, 2019.
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In this study we have measured the magnetoresistance response of inverted HgTe quantum wells in the presence of a large parallel magnetic field up to 33 T. We show that in quantum wells with inverted band structure a monotonically decreasing magnetoresistance is observed when a magnetic field up to the order of 10 T is applied parallel to the quantum well plane. This feature is accompanied by a vanishing of nonlocality and is consistent with a predicted modification of the energy spectrum that becomes gapless at a critical in-plane field Bc . Magnetic fields in excess of Bc allow us to investigate the evolution of the magnetoresistance in this field-induced semimetallic region beyond the known regime. After the longitudinal resistance reaches a minimum in the presumably gapless phase, we observe a strong upturn of the longitudinal resistance. A small residual Hall signal picked up in nonlocal measurements suggests that this feature is likely a bulk phenomenon and is caused by the semimetallicity of the sample. Theoretical calculations indeed support that the origin of these features is classical and a power law upturn of the resistance can be expected due to the specifics of two-carrier transport in thin (semi)metallic samples subjected to large magnetic fields.

@article{khouri2019magnetoresistance, abstract = {In this study we have measured the magnetoresistance response of inverted HgTe quantum wells in the presence of a large parallel magnetic field up to 33 T. We show that in quantum wells with inverted band structure a monotonically decreasing magnetoresistance is observed when a magnetic field up to the order of 10 T is applied parallel to the quantum well plane. This feature is accompanied by a vanishing of nonlocality and is consistent with a predicted modification of the energy spectrum that becomes gapless at a critical in-plane field Bc . Magnetic fields in excess of Bc allow us to investigate the evolution of the magnetoresistance in this field-induced semimetallic region beyond the known regime. After the longitudinal resistance reaches a minimum in the presumably gapless phase, we observe a strong upturn of the longitudinal resistance. A small residual Hall signal picked up in nonlocal measurements suggests that this feature is likely a bulk phenomenon and is caused by the semimetallicity of the sample. Theoretical calculations indeed support that the origin of these features is classical and a power law upturn of the resistance can be expected due to the specifics of two-carrier transport in thin (semi)metallic samples subjected to large magnetic fields.}, author = {Khouri, T. and Pezzini, S. and Bendias, M. and Leubner, P. and Zeitler, U. and Hussey, N. E. and Buhmann, H. and Molenkamp, L. W. and Titov, M. and Wiedmann, S.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {02}, number = 7, pages = {075303}, publisher = {American Physical Society}, title = {Magnetoresistance in the in-plane magnetic field induced semimetallic phase of inverted HgTe quantum wells}, volume = 99, year = 2019 }

%0 Journal Article %1 khouri2019magnetoresistance %A Khouri, T. %A Pezzini, S. %A Bendias, M. %A Leubner, P. %A Zeitler, U. %A Hussey, N. E. %A Buhmann, H. %A Molenkamp, L. W. %A Titov, M. %A Wiedmann, S. %D 2019 %I American Physical Society %J Phys. Rev. B %N 7 %P 075303 %R 10.1103/PhysRevB.99.075303 %T Magnetoresistance in the in-plane magnetic field induced semimetallic phase of inverted HgTe quantum wells %V 99 %X In this study we have measured the magnetoresistance response of inverted HgTe quantum wells in the presence of a large parallel magnetic field up to 33 T. We show that in quantum wells with inverted band structure a monotonically decreasing magnetoresistance is observed when a magnetic field up to the order of 10 T is applied parallel to the quantum well plane. This feature is accompanied by a vanishing of nonlocality and is consistent with a predicted modification of the energy spectrum that becomes gapless at a critical in-plane field Bc . Magnetic fields in excess of Bc allow us to investigate the evolution of the magnetoresistance in this field-induced semimetallic region beyond the known regime. After the longitudinal resistance reaches a minimum in the presumably gapless phase, we observe a strong upturn of the longitudinal resistance. A small residual Hall signal picked up in nonlocal measurements suggests that this feature is likely a bulk phenomenon and is caused by the semimetallicity of the sample. Theoretical calculations indeed support that the origin of these features is classical and a power law upturn of the resistance can be expected due to the specifics of two-carrier transport in thin (semi)metallic samples subjected to large magnetic fields.

High Mobility {HgTe} Microstructures for Quantum Spin Hall Studies. Bendias, Kalle; Shamim, Saquib; Herrmann, Oliver; Budewitz, Andreas; Shekhar, Pragya; Leubner, Philipp; Kleinlein, Johannes; Bocquillon, Erwann; Buhmann, Hartmut; Molenkamp, Laurens W. In Nano Letters, 18(8), pp. 4831–4836. American Chemical Society ({ACS}), 2018.
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The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities μ up to about 400 × 10^3 cm^2/(V s), and the mean free path λmfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.

@article{bendias2018mobility, abstract = {The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities μ up to about 400 × 10^3 cm^2/(V s), and the mean free path λmfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.}, author = {Bendias, Kalle and Shamim, Saquib and Herrmann, Oliver and Budewitz, Andreas and Shekhar, Pragya and Leubner, Philipp and Kleinlein, Johannes and Bocquillon, Erwann and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nano Letters}, keywords = {qt}, month = {07}, number = 8, pages = {4831–4836}, publisher = {American Chemical Society ({ACS})}, title = {High Mobility {HgTe} Microstructures for Quantum Spin Hall Studies}, volume = 18, year = 2018 }

%0 Journal Article %1 bendias2018mobility %A Bendias, Kalle %A Shamim, Saquib %A Herrmann, Oliver %A Budewitz, Andreas %A Shekhar, Pragya %A Leubner, Philipp %A Kleinlein, Johannes %A Bocquillon, Erwann %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2018 %I American Chemical Society ({ACS}) %J Nano Letters %N 8 %P 4831--4836 %R 10.1021/acs.nanolett.8b01405 %T High Mobility {HgTe} Microstructures for Quantum Spin Hall Studies %V 18 %X The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities μ up to about 400 × 10^3 cm^2/(V s), and the mean free path λmfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.
Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions. Bocquillon, E; Wiedenmann, J; Deacon, R. S.; Klapwijk, T. M.; Buhmann, H.; Molenkamp, L. W. In Topological Matter. Springer Series in Solid-State Sciences, 190, pp. 115–148. 2018.
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The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task, and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this chapter, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook toward more advanced microwave spectroscopy experiments, currently under development.

@article{bocquillon2018microwave, abstract = {The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task, and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this chapter, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook toward more advanced microwave spectroscopy experiments, currently under development.}, author = {Bocquillon, E and Wiedenmann, J and Deacon, R. S. and Klapwijk, T. M. and Buhmann, H. and Molenkamp, L. W.}, journal = {Topological Matter. Springer Series in Solid-State Sciences}, keywords = {qt}, pages = {115-148}, title = {Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions}, volume = 190, year = 2018 }

%0 Journal Article %1 bocquillon2018microwave %A Bocquillon, E %A Wiedenmann, J %A Deacon, R. S. %A Klapwijk, T. M. %A Buhmann, H. %A Molenkamp, L. W. %D 2018 %J Topological Matter. Springer Series in Solid-State Sciences %P 115-148 %R 10.1007/978-3-319-76388-0_5 %T Microwave Studies of the Fractional Josephson Effect in HgTe-Based Josephson Junctions %V 190 %X The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task, and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this chapter, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook toward more advanced microwave spectroscopy experiments, currently under development.

Interplay of Chiral and Helical States in a Quantum Spin Hall Insulator Lateral Junction. Calvo, M. R.; de Juan, F.; Ilan, R.; Fox, E. J.; Bestwick, A. J.; Mühlbauer, M.; Wang, J.; Ames, C.; Leubner, P.; Brüne, C.; Zhang, S. C.; Buhmann, H.; Molenkamp, L. W.; Goldhaber-Gordon, D. In Phys. Rev. Lett., 119(22), p. 226401. American Physical Society, 2017.
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We study the electronic transport across an electrostatically gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without an applied magnetic field. We control the carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the bulk gap, the magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus that reflect the equilibration between 1D chiral modes across the junction. As the carrier density approaches zero in the central region and at moderate fields, we observe oscillations in the resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.

@article{calvo2017interplay, abstract = {We study the electronic transport across an electrostatically gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without an applied magnetic field. We control the carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the bulk gap, the magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus that reflect the equilibration between 1D chiral modes across the junction. As the carrier density approaches zero in the central region and at moderate fields, we observe oscillations in the resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.}, author = {Calvo, M. R. and de Juan, F. and Ilan, R. and Fox, E. J. and Bestwick, A. J. and M\"uhlbauer, M. and Wang, J. and Ames, C. and Leubner, P. and Br\"une, C. and Zhang, S. C. and Buhmann, H. and Molenkamp, L. W. and Goldhaber-Gordon, D.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = 11, number = 22, pages = 226401, publisher = {American Physical Society}, title = {Interplay of Chiral and Helical States in a Quantum Spin Hall Insulator Lateral Junction}, volume = 119, year = 2017 }

%0 Journal Article %1 calvo2017interplay %A Calvo, M. R. %A de Juan, F. %A Ilan, R. %A Fox, E. J. %A Bestwick, A. J. %A Mühlbauer, M. %A Wang, J. %A Ames, C. %A Leubner, P. %A Brüne, C. %A Zhang, S. C. %A Buhmann, H. %A Molenkamp, L. W. %A Goldhaber-Gordon, D. %D 2017 %I American Physical Society %J Phys. Rev. Lett. %N 22 %P 226401 %R 10.1103/PhysRevLett.119.226401 %T Interplay of Chiral and Helical States in a Quantum Spin Hall Insulator Lateral Junction %V 119 %X We study the electronic transport across an electrostatically gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without an applied magnetic field. We control the carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the bulk gap, the magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus that reflect the equilibration between 1D chiral modes across the junction. As the carrier density approaches zero in the central region and at moderate fields, we observe oscillations in the resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.
Observation of Volkov-Pankratov states in topological HgTe heterojunctions using high-frequency compressibility. Inhofer, A.; Tchoumakov, S.; Assaf, B. A.; Fève, G.; Berroir, J. M.; Jouffrey, V.; Carpentier, D.; Goerbig, M. O.; Pla\ifmmode \mboxç\else \c{c}\fi{}ais, B.; Bendias, K.; Mahler, D. M.; Bocquillon, E.; Schlereth, R.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 96(19), p. 195104. American Physical Society, 2017.
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It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. We report on a set of experimental observations supporting the existence of additional massive surface states. These states are also confined by the band inversion at a topological-trivial semiconductor heterojunction. While first introduced by Volkov and Pankratov (VP) before the understanding of the topological nature of such a junction, they were not experimentally identified. Here we identify their signatures on transport properties at high electric field. By monitoring the ac admittance of HgTe topological-insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energies and electric fields. The Dirac states are characterized by a compressibility minimum, a linear energy dependence, and a high mobility persisting up to energies much larger than the transport band gap of the bulk. At higher energies, we observe multiple anomalous behaviors in conductance, charge metastability, and Hall resistance that point towards the contribution of massive surface states in transport scattering and charge transfer to the bulk. The spectrum of these anomalies agrees with predictions of a phenomenological model of VP states in a smooth topological heterojunction. The model accounts for the finite interface depth, the effect of electric fields including Dirac screening, and predicts the energy of the first VP state. The massive surface states are a hallmark of topological heterojunctions, whose understanding is crucial for transport studies and applications.

@article{inhofer2017observation, abstract = {It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. We report on a set of experimental observations supporting the existence of additional massive surface states. These states are also confined by the band inversion at a topological-trivial semiconductor heterojunction. While first introduced by Volkov and Pankratov (VP) before the understanding of the topological nature of such a junction, they were not experimentally identified. Here we identify their signatures on transport properties at high electric field. By monitoring the ac admittance of HgTe topological-insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energies and electric fields. The Dirac states are characterized by a compressibility minimum, a linear energy dependence, and a high mobility persisting up to energies much larger than the transport band gap of the bulk. At higher energies, we observe multiple anomalous behaviors in conductance, charge metastability, and Hall resistance that point towards the contribution of massive surface states in transport scattering and charge transfer to the bulk. The spectrum of these anomalies agrees with predictions of a phenomenological model of VP states in a smooth topological heterojunction. The model accounts for the finite interface depth, the effect of electric fields including Dirac screening, and predicts the energy of the first VP state. The massive surface states are a hallmark of topological heterojunctions, whose understanding is crucial for transport studies and applications.}, author = {Inhofer, A. and Tchoumakov, S. and Assaf, B. A. and F\`eve, G. and Berroir, J. M. and Jouffrey, V. and Carpentier, D. and Goerbig, M. O. and Pla\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ais, B. and Bendias, K. and Mahler, D. M. and Bocquillon, E. and Schlereth, R. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 11, number = 19, pages = 195104, publisher = {American Physical Society}, title = {Observation of Volkov-Pankratov states in topological HgTe heterojunctions using high-frequency compressibility}, volume = 96, year = 2017 }

%0 Journal Article %1 inhofer2017observation %A Inhofer, A. %A Tchoumakov, S. %A Assaf, B. A. %A Fève, G. %A Berroir, J. M. %A Jouffrey, V. %A Carpentier, D. %A Goerbig, M. O. %A Pla\ifmmode \mboxç\else \c{c}\fi{}ais, B. %A Bendias, K. %A Mahler, D. M. %A Bocquillon, E. %A Schlereth, R. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2017 %I American Physical Society %J Phys. Rev. B %N 19 %P 195104 %R 10.1103/PhysRevB.96.195104 %T Observation of Volkov-Pankratov states in topological HgTe heterojunctions using high-frequency compressibility %V 96 %X It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. We report on a set of experimental observations supporting the existence of additional massive surface states. These states are also confined by the band inversion at a topological-trivial semiconductor heterojunction. While first introduced by Volkov and Pankratov (VP) before the understanding of the topological nature of such a junction, they were not experimentally identified. Here we identify their signatures on transport properties at high electric field. By monitoring the ac admittance of HgTe topological-insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energies and electric fields. The Dirac states are characterized by a compressibility minimum, a linear energy dependence, and a high mobility persisting up to energies much larger than the transport band gap of the bulk. At higher energies, we observe multiple anomalous behaviors in conductance, charge metastability, and Hall resistance that point towards the contribution of massive surface states in transport scattering and charge transfer to the bulk. The spectrum of these anomalies agrees with predictions of a phenomenological model of VP states in a smooth topological heterojunction. The model accounts for the finite interface depth, the effect of electric fields including Dirac screening, and predicts the energy of the first VP state. The massive surface states are a hallmark of topological heterojunctions, whose understanding is crucial for transport studies and applications.
Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe. Wiedenmann, Jonas; Liebhaber, Eva; Kübert, Johannes; Bocquillon, Erwann; Burset, Pablo; Ames, Christopher; Buhmann, Hartmut; Klapwijk, Teun M.; Molenkamp, Laurens W. In Phys. Rev. B, 96(16), p. 165302. American Physical Society, 2017.
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The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.

@article{wiedenmann2017transport, abstract = {The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.}, author = {Wiedenmann, Jonas and Liebhaber, Eva and K\"ubert, Johannes and Bocquillon, Erwann and Burset, Pablo and Ames, Christopher and Buhmann, Hartmut and Klapwijk, Teun M. and Molenkamp, Laurens W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 10, number = 16, pages = 165302, publisher = {American Physical Society}, title = {Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe}, volume = 96, year = 2017 }

%0 Journal Article %1 wiedenmann2017transport %A Wiedenmann, Jonas %A Liebhaber, Eva %A Kübert, Johannes %A Bocquillon, Erwann %A Burset, Pablo %A Ames, Christopher %A Buhmann, Hartmut %A Klapwijk, Teun M. %A Molenkamp, Laurens W. %D 2017 %I American Physical Society %J Phys. Rev. B %N 16 %P 165302 %R 10.1103/PhysRevB.96.165302 %T Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe %V 96 %X The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.
Controlled finite momentum pairing and spatially varying order parameter in proximitized {HgTe} quantum wells. Hart, Sean; Ren, Hechen; Kosowsky, Michael; Ben-Shach, Gilad; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Halperin, Bertrand I.; Yacoby, Amir. In Nature Physics, 13(1), pp. 87–93. Springer Science and Business Media {LLC}, 2017.
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Conventional s-wave superconductivity arises from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs with zero net momentum. Recent studies have focused on coupling s-wave superconductors to systems with an unusual configuration of electronic spin and momentum at the Fermi surface, where the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of HgTe quantum wells coupled to aluminium or niobium superconductors and subject to a magnetic field in the plane of the quantum well. We find that this magnetic field tunes the momentum of Cooper pairs in the quantum well, directly reflecting the response of the spin-dependent Fermi surfaces. In the high electron density regime, the induced superconductivity evolves with electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes and Zhang. This agreement provides a quantitative value for g ̃/vF, where g ̃ is the effective g-factor and vF is the Fermi velocity. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter from singlet to triplet pairing, and in general allows investigation of electronic spin texture at the Fermi surface of materials.

@article{hart2017controlled, abstract = {Conventional s-wave superconductivity arises from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs with zero net momentum. Recent studies have focused on coupling s-wave superconductors to systems with an unusual configuration of electronic spin and momentum at the Fermi surface, where the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of HgTe quantum wells coupled to aluminium or niobium superconductors and subject to a magnetic field in the plane of the quantum well. We find that this magnetic field tunes the momentum of Cooper pairs in the quantum well, directly reflecting the response of the spin-dependent Fermi surfaces. In the high electron density regime, the induced superconductivity evolves with electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes and Zhang. This agreement provides a quantitative value for g ̃/vF, where g ̃ is the effective g-factor and vF is the Fermi velocity. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter from singlet to triplet pairing, and in general allows investigation of electronic spin texture at the Fermi surface of materials.}, author = {Hart, Sean and Ren, Hechen and Kosowsky, Michael and Ben-Shach, Gilad and Leubner, Philipp and Brüne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Halperin, Bertrand I. and Yacoby, Amir}, journal = {Nature Physics}, keywords = {qt}, month = {09}, number = 1, pages = {87–93}, publisher = {Springer Science and Business Media {LLC}}, title = {Controlled finite momentum pairing and spatially varying order parameter in proximitized {HgTe} quantum wells}, volume = 13, year = 2017 }

%0 Journal Article %1 hart2017controlled %A Hart, Sean %A Ren, Hechen %A Kosowsky, Michael %A Ben-Shach, Gilad %A Leubner, Philipp %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Halperin, Bertrand I. %A Yacoby, Amir %D 2017 %I Springer Science and Business Media {LLC} %J Nature Physics %N 1 %P 87--93 %R 10.1038/nphys3877 %T Controlled finite momentum pairing and spatially varying order parameter in proximitized {HgTe} quantum wells %V 13 %X Conventional s-wave superconductivity arises from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs with zero net momentum. Recent studies have focused on coupling s-wave superconductors to systems with an unusual configuration of electronic spin and momentum at the Fermi surface, where the nature of the paired state can be modified and the system may even undergo a topological phase transition. Here we present measurements and theoretical calculations of HgTe quantum wells coupled to aluminium or niobium superconductors and subject to a magnetic field in the plane of the quantum well. We find that this magnetic field tunes the momentum of Cooper pairs in the quantum well, directly reflecting the response of the spin-dependent Fermi surfaces. In the high electron density regime, the induced superconductivity evolves with electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes and Zhang. This agreement provides a quantitative value for g ̃/vF, where g ̃ is the effective g-factor and vF is the Fermi velocity. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter from singlet to triplet pairing, and in general allows investigation of electronic spin texture at the Fermi surface of materials.
CdTe-HgTe core-shell nanowire growth controlled by RHEED. Kessel, M.; Hajer, J.; Karczewski, G.; Schumacher, C.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Materials, 1(2), p. 023401. American Physical Society, 2017.
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We present results on the growth of CdTe-HgTe core-shell nanowires, a realization of a quasi-one-dimensional heterostructure of the topological insulator HgTe. The growth is a two step process consisting of the growth of single crystalline zinc blende CdTe nanowires with the vapor-liquid-solid method and the overgrowth of these wires with HgTe such that a closed shell is formed around the CdTe core structure. The CdTe wire growth is monitored by RHEED allowing us to infer information on the crystal properties from the electron diffraction pattern. This information is used to find and control the optimal growth temperature. High quality single crystal CdTe nanowires grow with a preferred orientation. For the growth of the conductive HgTe shell structure we find that the supplied Hg:Te ratio is the crucial parameter to facilitate growth on all surface facets.

@article{kessel2017cdtehgte, abstract = {We present results on the growth of CdTe-HgTe core-shell nanowires, a realization of a quasi-one-dimensional heterostructure of the topological insulator HgTe. The growth is a two step process consisting of the growth of single crystalline zinc blende CdTe nanowires with the vapor-liquid-solid method and the overgrowth of these wires with HgTe such that a closed shell is formed around the CdTe core structure. The CdTe wire growth is monitored by RHEED allowing us to infer information on the crystal properties from the electron diffraction pattern. This information is used to find and control the optimal growth temperature. High quality single crystal CdTe nanowires grow with a preferred orientation. For the growth of the conductive HgTe shell structure we find that the supplied Hg:Te ratio is the crucial parameter to facilitate growth on all surface facets.}, author = {Kessel, M. and Hajer, J. and Karczewski, G. and Schumacher, C. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. Materials}, keywords = {qt}, month = {07}, number = 2, pages = {023401}, publisher = {American Physical Society}, title = {CdTe-HgTe core-shell nanowire growth controlled by RHEED}, volume = 1, year = 2017 }

%0 Journal Article %1 kessel2017cdtehgte %A Kessel, M. %A Hajer, J. %A Karczewski, G. %A Schumacher, C. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2017 %I American Physical Society %J Phys. Rev. Materials %N 2 %P 023401 %R 10.1103/PhysRevMaterials.1.023401 %T CdTe-HgTe core-shell nanowire growth controlled by RHEED %V 1 %X We present results on the growth of CdTe-HgTe core-shell nanowires, a realization of a quasi-one-dimensional heterostructure of the topological insulator HgTe. The growth is a two step process consisting of the growth of single crystalline zinc blende CdTe nanowires with the vapor-liquid-solid method and the overgrowth of these wires with HgTe such that a closed shell is formed around the CdTe core structure. The CdTe wire growth is monitored by RHEED allowing us to infer information on the crystal properties from the electron diffraction pattern. This information is used to find and control the optimal growth temperature. High quality single crystal CdTe nanowires grow with a preferred orientation. For the growth of the conductive HgTe shell structure we find that the supplied Hg:Te ratio is the crucial parameter to facilitate growth on all surface facets.
Observation of the universal magnetoelectric effect in a 3D topological insulator. Dziom, V.; Shuvaev, A.; Pimenov, A.; Astakhov, G. V.; Ames, C.; Bendias, K.; Böttcher, J.; Tkachov, G.; Hankiewicz, E. M.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Nature Communications, 8(1). Springer Science and Business Media {LLC}, 2017.
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The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

@article{dziom2017observation, abstract = {The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.}, author = {Dziom, V. and Shuvaev, A. and Pimenov, A. and Astakhov, G. V. and Ames, C. and Bendias, K. and Böttcher, J. and Tkachov, G. and Hankiewicz, E. M. and Brüne, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Nature Communications}, keywords = {qt}, month = {05}, number = 1, publisher = {Springer Science and Business Media {LLC}}, title = {Observation of the universal magnetoelectric effect in a 3D topological insulator}, volume = 8, year = 2017 }

%0 Journal Article %1 dziom2017observation %A Dziom, V. %A Shuvaev, A. %A Pimenov, A. %A Astakhov, G. V. %A Ames, C. %A Bendias, K. %A Böttcher, J. %A Tkachov, G. %A Hankiewicz, E. M. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2017 %I Springer Science and Business Media {LLC} %J Nature Communications %N 1 %R 10.1038/ncomms15197 %T Observation of the universal magnetoelectric effect in a 3D topological insulator %V 8 %X The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
Josephson Radiation from Gapless Andreev Bound States in HgTe-Based Topological Junctions. Deacon, R. S.; Wiedenmann, J.; Bocquillon, E.; Dom\’{\i}nguez, F.; Klapwijk, T. M.; Leubner, P.; Brüne, C.; Hankiewicz, E. M.; Tarucha, S.; Ishibashi, K.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. X, 7(2), p. 021011. American Physical Society, 2017.
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Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency fJ rather than conventional emission at fJ. Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency fJ/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the fJ/2 line, much shorter than for the fJ line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.

@article{deacon2017josephson, abstract = {Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency fJ rather than conventional emission at fJ. Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency fJ/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the fJ/2 line, much shorter than for the fJ line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.}, author = {Deacon, R. S. and Wiedenmann, J. and Bocquillon, E. and Dom\'{\i}nguez, F. and Klapwijk, T. M. and Leubner, P. and Br\"une, C. and Hankiewicz, E. M. and Tarucha, S. and Ishibashi, K. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. X}, keywords = {qt}, month = {04}, number = 2, pages = {021011}, publisher = {American Physical Society}, title = {Josephson Radiation from Gapless Andreev Bound States in HgTe-Based Topological Junctions}, volume = 7, year = 2017 }

%0 Journal Article %1 deacon2017josephson %A Deacon, R. S. %A Wiedenmann, J. %A Bocquillon, E. %A Dom\'{\i}nguez, F. %A Klapwijk, T. M. %A Leubner, P. %A Brüne, C. %A Hankiewicz, E. M. %A Tarucha, S. %A Ishibashi, K. %A Buhmann, H. %A Molenkamp, L. W. %D 2017 %I American Physical Society %J Phys. Rev. X %N 2 %P 021011 %R 10.1103/PhysRevX.7.021011 %T Josephson Radiation from Gapless Andreev Bound States in HgTe-Based Topological Junctions %V 7 %X Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency fJ rather than conventional emission at fJ. Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency fJ/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the fJ/2 line, much shorter than for the fJ line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.
Electron–hole asymmetry of the topological surface states in strained HgTe. Jost, Andreas; Bendias, Michel; Böttcher, Jan; Hankiewicz, Ewelina; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Maan, Jan C.; Zeitler, Uli; Hussey, Nigel; Steffen, Wiedmann. In PNAS, 9(13), pp. 3381–3386. 2017.
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Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron–hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected.

@article{jost2017electronhole, abstract = {Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron–hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected.}, author = {Jost, Andreas and Bendias, Michel and Böttcher, Jan and Hankiewicz, Ewelina and Brüne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Maan, Jan C. and Zeitler, Uli and Hussey, Nigel and Steffen, Wiedmann}, journal = {PNAS}, keywords = {qt}, month = {03}, number = 13, pages = {3381-3386}, title = {Electron–hole asymmetry of the topological surface states in strained HgTe}, volume = 9, year = 2017 }

%0 Journal Article %1 jost2017electronhole %A Jost, Andreas %A Bendias, Michel %A Böttcher, Jan %A Hankiewicz, Ewelina %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Maan, Jan C. %A Zeitler, Uli %A Hussey, Nigel %A Steffen, Wiedmann %D 2017 %J PNAS %N 13 %P 3381-3386 %R https://doi.org/10.1073/pnas.1611663114 %T Electron–hole asymmetry of the topological surface states in strained HgTe %V 9 %X Topological insulators are a new class of materials with an insulating bulk and topologically protected metallic surface states. Although it is widely assumed that these surface states display a Dirac-type dispersion that is symmetric above and below the Dirac point, this exact equivalence across the Fermi level has yet to be established experimentally. Here, we present a detailed transport study of the 3D topological insulator-strained HgTe that strongly challenges this prevailing viewpoint. First, we establish the existence of exclusively surface-dominated transport via the observation of an ambipolar surface quantum Hall effect and quantum oscillations in the Seebeck and Nernst effect. Second, we show that, whereas the thermopower is diffusion driven for surface electrons, both diffusion and phonon drag contributions are essential for the hole surface carriers. This distinct behavior in the thermoelectric response is explained by a strong deviation from the linear dispersion relation for the surface states, with a much flatter dispersion for holes compared with electrons. These findings show that the metallic surface states in topological insulators can exhibit both strong electron–hole asymmetry and a strong deviation from a linear dispersion but remain topologically protected.

Thermoelectrics with Coulomb-coupled quantum dots. Thierschmann, Holger; S{{á}}nchez, Rafael; Sothmann, Björn; Buhmann, Hartmut; Molenkamp, Laurens W. In Comptes Rendus Physique, 17(10), pp. 1109–1122. Elsevier {BV}, 2016.
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In this article we review the thermoelectric properties of three terminal devices with Coulomb-coupled quantum dots (QDs) as observed in recent experiments. The system we consider consists of two Coulomb-blockade QDs, one of which can exchange electrons with only a single reservoir (heat reservoir), while the other dot is tunnel coupled with two reservoirs at a lower temperature (conductor). The heat reservoir and the conductor interact only via the Coulomb coupling of the quantum dots. It has been found that two regimes have to be considered. In the first one, the heat flow between the two systems is small. In this regime, thermally driven occupation fluctuations of the hot QD modify the transport properties of the conductor system. This leads to an effect called thermal gating. Experiments have shown how this can be used to control charge flow in the conductor by means of temperature in a remote reservoir. We further substantiate the observations with model calculations, and implications for the realisation of an all-thermal transistor are discussed. In the second regime, the heat flow between the two systems is relevant. Here the system works as a nanoscale heat engine, as proposed recently (Sánchez and Büttiker). We review the conceptual idea, its experimental realisation and the novel features arising in this new kind of thermoelectric device such as decoupling of heat and charge flow.

@article{thierschmann2016thermoelectrics, abstract = {In this article we review the thermoelectric properties of three terminal devices with Coulomb-coupled quantum dots (QDs) as observed in recent experiments. The system we consider consists of two Coulomb-blockade QDs, one of which can exchange electrons with only a single reservoir (heat reservoir), while the other dot is tunnel coupled with two reservoirs at a lower temperature (conductor). The heat reservoir and the conductor interact only via the Coulomb coupling of the quantum dots. It has been found that two regimes have to be considered. In the first one, the heat flow between the two systems is small. In this regime, thermally driven occupation fluctuations of the hot QD modify the transport properties of the conductor system. This leads to an effect called thermal gating. Experiments have shown how this can be used to control charge flow in the conductor by means of temperature in a remote reservoir. We further substantiate the observations with model calculations, and implications for the realisation of an all-thermal transistor are discussed. In the second regime, the heat flow between the two systems is relevant. Here the system works as a nanoscale heat engine, as proposed recently (Sánchez and Büttiker). We review the conceptual idea, its experimental realisation and the novel features arising in this new kind of thermoelectric device such as decoupling of heat and charge flow.}, author = {Thierschmann, Holger and S{\'{a}}nchez, Rafael and Sothmann, Björn and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Comptes Rendus Physique}, keywords = {qt}, month = 12, number = 10, pages = {1109–1122}, publisher = {Elsevier {BV}}, title = {Thermoelectrics with Coulomb-coupled quantum dots}, volume = 17, year = 2016 }

%0 Journal Article %1 thierschmann2016thermoelectrics %A Thierschmann, Holger %A S{{á}}nchez, Rafael %A Sothmann, Björn %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2016 %I Elsevier {BV} %J Comptes Rendus Physique %N 10 %P 1109--1122 %R 10.1016/j.crhy.2016.08.001 %T Thermoelectrics with Coulomb-coupled quantum dots %V 17 %X In this article we review the thermoelectric properties of three terminal devices with Coulomb-coupled quantum dots (QDs) as observed in recent experiments. The system we consider consists of two Coulomb-blockade QDs, one of which can exchange electrons with only a single reservoir (heat reservoir), while the other dot is tunnel coupled with two reservoirs at a lower temperature (conductor). The heat reservoir and the conductor interact only via the Coulomb coupling of the quantum dots. It has been found that two regimes have to be considered. In the first one, the heat flow between the two systems is small. In this regime, thermally driven occupation fluctuations of the hot QD modify the transport properties of the conductor system. This leads to an effect called thermal gating. Experiments have shown how this can be used to control charge flow in the conductor by means of temperature in a remote reservoir. We further substantiate the observations with model calculations, and implications for the realisation of an all-thermal transistor are discussed. In the second regime, the heat flow between the two systems is relevant. Here the system works as a nanoscale heat engine, as proposed recently (Sánchez and Büttiker). We review the conceptual idea, its experimental realisation and the novel features arising in this new kind of thermoelectric device such as decoupling of heat and charge flow.
Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. Wiedmann, S.; Jost, A.; Fauqué, B.; van Dijk, J.; Meijer, M. J.; Khouri, T.; Pezzini, S.; Grauer, S.; Schreyeck, S.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; Hussey, N. E. In Phys. Rev. B, 94(8), p. 081302. American Physical Society, 2016.
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We report on high-field angle-dependent magnetotransport measurements on epitaxial thin films of Bi2Se3, a three-dimensional topological insulator. At low temperature, we observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. The magnetoresistance of Bi2Se3 is found to be highly anisotropic. In the presence of a parallel electric and magnetic field, we observe a strong negative longitudinal magnetoresistance that has been considered as a smoking gun for the presence of chiral fermions in a certain class of semimetals due to the so-called axial anomaly. Its observation in a three-dimensional topological insulator implies that the axial anomaly may be in fact a far more generic phenomenon than originally thought.

@article{wiedmann2016anisotropic, abstract = {We report on high-field angle-dependent magnetotransport measurements on epitaxial thin films of Bi2Se3, a three-dimensional topological insulator. At low temperature, we observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. The magnetoresistance of Bi2Se3 is found to be highly anisotropic. In the presence of a parallel electric and magnetic field, we observe a strong negative longitudinal magnetoresistance that has been considered as a smoking gun for the presence of chiral fermions in a certain class of semimetals due to the so-called axial anomaly. Its observation in a three-dimensional topological insulator implies that the axial anomaly may be in fact a far more generic phenomenon than originally thought.}, author = {Wiedmann, S. and Jost, A. and Fauqu\'e, B. and van Dijk, J. and Meijer, M. J. and Khouri, T. and Pezzini, S. and Grauer, S. and Schreyeck, S. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W. and Hussey, N. E.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {08}, number = 8, pages = {081302}, publisher = {American Physical Society}, title = {Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$}, volume = 94, year = 2016 }

%0 Journal Article %1 wiedmann2016anisotropic %A Wiedmann, S. %A Jost, A. %A Fauqué, B. %A van Dijk, J. %A Meijer, M. J. %A Khouri, T. %A Pezzini, S. %A Grauer, S. %A Schreyeck, S. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %A Hussey, N. E. %D 2016 %I American Physical Society %J Phys. Rev. B %N 8 %P 081302 %R 10.1103/PhysRevB.94.081302 %T Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ %V 94 %X We report on high-field angle-dependent magnetotransport measurements on epitaxial thin films of Bi2Se3, a three-dimensional topological insulator. At low temperature, we observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. The magnetoresistance of Bi2Se3 is found to be highly anisotropic. In the presence of a parallel electric and magnetic field, we observe a strong negative longitudinal magnetoresistance that has been considered as a smoking gun for the presence of chiral fermions in a certain class of semimetals due to the so-called axial anomaly. Its observation in a three-dimensional topological insulator implies that the axial anomaly may be in fact a far more generic phenomenon than originally thought.
Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates. Leubner, Philipp; Lunczer, Lukas; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W. In Phys. Rev. Lett., 117(8), p. 086403. American Physical Society, 2016.
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The HgTe quantum well (QW) is a well-characterized two-dimensional topological insulator (2D TI). Its band gap is relatively small (typically on the order of 10 meV), which restricts the observation of purely topological conductance to low temperatures. Here, we utilize the strain dependence of the band structure of HgTe QWs to address this limitation. We use CdTe−Cd0.5Zn0.5Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magnetotransport measurements, which demonstrate a transition from a semimetallic to a 2D-TI regime in wide QWs, when the strain is changed from tensile to compressive. Most notably, we demonstrate a much enhanced energy gap of 55 meV in heavily compressively strained QWs. This value exceeds the highest possible gap on common II-VI substrates by a factor of 2–3, and extends the regime where the topological conductance prevails to much higher temperatures.

@article{leubner2016strain, abstract = {The HgTe quantum well (QW) is a well-characterized two-dimensional topological insulator (2D TI). Its band gap is relatively small (typically on the order of 10 meV), which restricts the observation of purely topological conductance to low temperatures. Here, we utilize the strain dependence of the band structure of HgTe QWs to address this limitation. We use CdTe−Cd0.5Zn0.5Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magnetotransport measurements, which demonstrate a transition from a semimetallic to a 2D-TI regime in wide QWs, when the strain is changed from tensile to compressive. Most notably, we demonstrate a much enhanced energy gap of 55 meV in heavily compressively strained QWs. This value exceeds the highest possible gap on common II-VI substrates by a factor of 2–3, and extends the regime where the topological conductance prevails to much higher temperatures.}, author = {Leubner, Philipp and Lunczer, Lukas and Br\"une, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {08}, number = 8, pages = {086403}, publisher = {American Physical Society}, title = {Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates}, volume = 117, year = 2016 }

%0 Journal Article %1 leubner2016strain %A Leubner, Philipp %A Lunczer, Lukas %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2016 %I American Physical Society %J Phys. Rev. Lett. %N 8 %P 086403 %R 10.1103/PhysRevLett.117.086403 %T Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates %V 117 %X The HgTe quantum well (QW) is a well-characterized two-dimensional topological insulator (2D TI). Its band gap is relatively small (typically on the order of 10 meV), which restricts the observation of purely topological conductance to low temperatures. Here, we utilize the strain dependence of the band structure of HgTe QWs to address this limitation. We use CdTe−Cd0.5Zn0.5Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magnetotransport measurements, which demonstrate a transition from a semimetallic to a 2D-TI regime in wide QWs, when the strain is changed from tensile to compressive. Most notably, we demonstrate a much enhanced energy gap of 55 meV in heavily compressively strained QWs. This value exceeds the highest possible gap on common II-VI substrates by a factor of 2–3, and extends the regime where the topological conductance prevails to much higher temperatures.
Gapless Andreev bound states in the quantum spin Hall insulator {HgTe}. Bocquillon, Erwann; Deacon, Russell S.; Wiedenmann, Jonas; Leubner, Philipp; Klapwijk, Teunis M.; Brüne, Christoph; Ishibashi, Koji; Buhmann, Hartmut; Molenkamp, Laurens W. In Nature Nanotechnology, 12(2), pp. 137–143. Springer Nature, 2016.
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In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.

@article{bocquillon2016gapless, abstract = {In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.}, author = {Bocquillon, Erwann and Deacon, Russell S. and Wiedenmann, Jonas and Leubner, Philipp and Klapwijk, Teunis M. and Brüne, Christoph and Ishibashi, Koji and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nature Nanotechnology}, keywords = {qt}, month = {08}, number = 2, pages = {137–143}, publisher = {Springer Nature}, title = {Gapless Andreev bound states in the quantum spin Hall insulator {HgTe}}, volume = 12, year = 2016 }

%0 Journal Article %1 bocquillon2016gapless %A Bocquillon, Erwann %A Deacon, Russell S. %A Wiedenmann, Jonas %A Leubner, Philipp %A Klapwijk, Teunis M. %A Brüne, Christoph %A Ishibashi, Koji %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2016 %I Springer Nature %J Nature Nanotechnology %N 2 %P 137--143 %R 10.1038/nnano.2016.159 %T Gapless Andreev bound states in the quantum spin Hall insulator {HgTe} %V 12 %X In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.
High-temperature quantum Hall effect in finite gapped HgTe quantum wells. Khouri, T.; Bendias, M.; Leubner, P.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; Zeitler, U.; Hussey, N. E.; Wiedmann, S. In Phys. Rev. B, 93(12), p. 125308. American Physical Society, 2016.
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We report on the observation of the quantum Hall effect at high temperatures in HgTe quantum wells with a finite band gap and a thickness below and above the critical thickness dc that separates a conventional semiconductor from a two-dimensional topological insulator. At high carrier concentrations, we observe a quantized Hall conductivity up to 60 K with energy gaps between Landau levels of the order of 25 meV, in good agreement with the Landau level spectrum obtained from k⋅p calculations. Using the scaling approach for the plateau-plateau transition at ν=2→1, we find the scaling coefficient κ=0.45±0.04 to be consistent with the universality of scaling theory, and we do not find signs of increased electron-phonon interaction to alter the scaling even at these elevated temperatures. Comparing the high-temperature limit of the quantized Hall resistance in HgTe quantum wells with a finite band gap with room-temperature experiment in graphene, we find that the energy gaps at the breakdown of the quantization exceed the thermal energy by the same order of magnitude.

@article{khouri2016hightemperature, abstract = {We report on the observation of the quantum Hall effect at high temperatures in HgTe quantum wells with a finite band gap and a thickness below and above the critical thickness dc that separates a conventional semiconductor from a two-dimensional topological insulator. At high carrier concentrations, we observe a quantized Hall conductivity up to 60 K with energy gaps between Landau levels of the order of 25 meV, in good agreement with the Landau level spectrum obtained from k⋅p calculations. Using the scaling approach for the plateau-plateau transition at ν=2→1, we find the scaling coefficient κ=0.45±0.04 to be consistent with the universality of scaling theory, and we do not find signs of increased electron-phonon interaction to alter the scaling even at these elevated temperatures. Comparing the high-temperature limit of the quantized Hall resistance in HgTe quantum wells with a finite band gap with room-temperature experiment in graphene, we find that the energy gaps at the breakdown of the quantization exceed the thermal energy by the same order of magnitude.}, author = {Khouri, T. and Bendias, M. and Leubner, P. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W. and Zeitler, U. and Hussey, N. E. and Wiedmann, S.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {03}, number = 12, pages = 125308, publisher = {American Physical Society}, title = {High-temperature quantum Hall effect in finite gapped HgTe quantum wells}, volume = 93, year = 2016 }

%0 Journal Article %1 khouri2016hightemperature %A Khouri, T. %A Bendias, M. %A Leubner, P. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %A Zeitler, U. %A Hussey, N. E. %A Wiedmann, S. %D 2016 %I American Physical Society %J Phys. Rev. B %N 12 %P 125308 %R 10.1103/PhysRevB.93.125308 %T High-temperature quantum Hall effect in finite gapped HgTe quantum wells %V 93 %X We report on the observation of the quantum Hall effect at high temperatures in HgTe quantum wells with a finite band gap and a thickness below and above the critical thickness dc that separates a conventional semiconductor from a two-dimensional topological insulator. At high carrier concentrations, we observe a quantized Hall conductivity up to 60 K with energy gaps between Landau levels of the order of 25 meV, in good agreement with the Landau level spectrum obtained from k⋅p calculations. Using the scaling approach for the plateau-plateau transition at ν=2→1, we find the scaling coefficient κ=0.45±0.04 to be consistent with the universality of scaling theory, and we do not find signs of increased electron-phonon interaction to alter the scaling even at these elevated temperatures. Comparing the high-temperature limit of the quantized Hall resistance in HgTe quantum wells with a finite band gap with room-temperature experiment in graphene, we find that the energy gaps at the breakdown of the quantization exceed the thermal energy by the same order of magnitude.
4$\uppi$-periodic Josephson supercurrent in {HgTe}-based topological Josephson junctions. Wiedenmann, J.; Bocquillon, E.; Deacon, R. S.; Hartinger, S.; Herrmann, O.; Klapwijk, T. M.; Maier, L.; Ames, C.; Brüne, C.; Gould, C.; Oiwa, A.; Ishibashi, K.; Tarucha, S.; Buhmann, H.; Molenkamp, L. W. In Nature Communications, 7(1). Springer Science and Business Media {LLC}, 2016.
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The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4π-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4π-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator.

@article{Wiedenmann_2016, abstract = {The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4π-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4π-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator.}, author = {Wiedenmann, J. and Bocquillon, E. and Deacon, R. S. and Hartinger, S. and Herrmann, O. and Klapwijk, T. M. and Maier, L. and Ames, C. and Brüne, C. and Gould, C. and Oiwa, A. and Ishibashi, K. and Tarucha, S. and Buhmann, H. and Molenkamp, L. W.}, journal = {Nature Communications}, keywords = {qt}, month = {01}, number = 1, publisher = {Springer Science and Business Media {LLC}}, title = {4$\uppi$-periodic Josephson supercurrent in {HgTe}-based topological Josephson junctions}, volume = 7, year = 2016 }

%0 Journal Article %1 Wiedenmann_2016 %A Wiedenmann, J. %A Bocquillon, E. %A Deacon, R. S. %A Hartinger, S. %A Herrmann, O. %A Klapwijk, T. M. %A Maier, L. %A Ames, C. %A Brüne, C. %A Gould, C. %A Oiwa, A. %A Ishibashi, K. %A Tarucha, S. %A Buhmann, H. %A Molenkamp, L. W. %D 2016 %I Springer Science and Business Media {LLC} %J Nature Communications %N 1 %R 10.1038/ncomms10303 %T 4$\uppi$-periodic Josephson supercurrent in {HgTe}-based topological Josephson junctions %V 7 %X The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4π-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4π-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator.

Thermal control and generation of charge currents in coupled quantum dots. Thierschmann, Holger; Arnold, Fabian; Mittermüller, Marcel; Maier, Luis; Heyn, Christian; Hansen, Wolfang; Buhmann, Hartmut; Molenkamp, Laurens W. In physica status solidi (a), 213(3), pp. 582–590. Wiley, 2015.
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This article reviews recent thermoelectric experiments on quantum dot (QD) systems. The experiments focus on two types of inter‐dot coupling: tunnel coupling and Coulomb coupling. Tunnel‐coupled QDs allow particles to be exchanged between the attached reservoirs via the QD system. Hence, an applied temperature bias results in a thermovoltage. When being investigated as a function of QD energies, this leads to the thermopower stability diagram. Here, largest thermovoltage is observed in the regions of the triple points. In a QD system which exhibits only capacitive inter‐dot coupling, electron transfer is suppressed. Such a device is studied in a three‐terminal geometry: while one QD connects to the heat reservoir, the other one can exchange electrons with two reservoirs at a lower temperature. When the symmetry of the tunneling coefficients in the cold system is broken, the device becomes an energy harvester: thermal energy is extracted from the heat reservoir and is converted into a directed charge current between the two cold reservoirs. This review illustrates the large potential of multi‐QD devices for thermoelectrics and thermal management at the nanometer‐scale.

@article{thierschmann2015thermal, abstract = {This article reviews recent thermoelectric experiments on quantum dot (QD) systems. The experiments focus on two types of inter‐dot coupling: tunnel coupling and Coulomb coupling. Tunnel‐coupled QDs allow particles to be exchanged between the attached reservoirs via the QD system. Hence, an applied temperature bias results in a thermovoltage. When being investigated as a function of QD energies, this leads to the thermopower stability diagram. Here, largest thermovoltage is observed in the regions of the triple points. In a QD system which exhibits only capacitive inter‐dot coupling, electron transfer is suppressed. Such a device is studied in a three‐terminal geometry: while one QD connects to the heat reservoir, the other one can exchange electrons with two reservoirs at a lower temperature. When the symmetry of the tunneling coefficients in the cold system is broken, the device becomes an energy harvester: thermal energy is extracted from the heat reservoir and is converted into a directed charge current between the two cold reservoirs. This review illustrates the large potential of multi‐QD devices for thermoelectrics and thermal management at the nanometer‐scale.}, author = {Thierschmann, Holger and Arnold, Fabian and Mittermüller, Marcel and Maier, Luis and Heyn, Christian and Hansen, Wolfang and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {physica status solidi (a)}, keywords = {qt}, month = 12, number = 3, pages = {582–590}, publisher = {Wiley}, title = {Thermal control and generation of charge currents in coupled quantum dots}, volume = 213, year = 2015 }

%0 Journal Article %1 thierschmann2015thermal %A Thierschmann, Holger %A Arnold, Fabian %A Mittermüller, Marcel %A Maier, Luis %A Heyn, Christian %A Hansen, Wolfang %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2015 %I Wiley %J physica status solidi (a) %N 3 %P 582--590 %R 10.1002/pssa.201532608 %T Thermal control and generation of charge currents in coupled quantum dots %V 213 %X This article reviews recent thermoelectric experiments on quantum dot (QD) systems. The experiments focus on two types of inter‐dot coupling: tunnel coupling and Coulomb coupling. Tunnel‐coupled QDs allow particles to be exchanged between the attached reservoirs via the QD system. Hence, an applied temperature bias results in a thermovoltage. When being investigated as a function of QD energies, this leads to the thermopower stability diagram. Here, largest thermovoltage is observed in the regions of the triple points. In a QD system which exhibits only capacitive inter‐dot coupling, electron transfer is suppressed. Such a device is studied in a three‐terminal geometry: while one QD connects to the heat reservoir, the other one can exchange electrons with two reservoirs at a lower temperature. When the symmetry of the tunneling coefficients in the cold system is broken, the device becomes an energy harvester: thermal energy is extracted from the heat reservoir and is converted into a directed charge current between the two cold reservoirs. This review illustrates the large potential of multi‐QD devices for thermoelectrics and thermal management at the nanometer‐scale.
Thermoelectric efficiency in the linear transport regime. Eltschka, Christopher; Thierschmann, Holger; Buhmann, Hartmut; Siewert, Jens. In physica status solidi (a), 213(3), pp. 626–634. Wiley, 2015.
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Improving the efficiency of thermoelectric devices is a long‐term goal in thermoelectricity research. Deeper insight into the meaning of the related quantities, in particular the figure of merit is instrumental for progress in this direction. Here, we study the regime of linear transport where entirely general statements can be made for the electronic part of the thermoelectric efficiency. These results essentially do not depend on the type of device, its layout, or the involved transport mechanisms. For two‐terminal devices, where charge and heat currents flow along the same path, we find a particularly simple and intuitive expression for the figure of merit ZT. In multi‐terminal devices with different paths for the currents, the thermoelectric efficiency does not admit such a simple interpretation. Nonetheless, nontrivial device‐independent statements can be made about the efficiency. As a practical example, we consider the heat‐to‐current converter Sánchez and Büttiker, Phys. Rev. B 83, 085428 (2011).

@article{eltschka2015thermoelectric, abstract = {Improving the efficiency of thermoelectric devices is a long‐term goal in thermoelectricity research. Deeper insight into the meaning of the related quantities, in particular the figure of merit is instrumental for progress in this direction. Here, we study the regime of linear transport where entirely general statements can be made for the electronic part of the thermoelectric efficiency. These results essentially do not depend on the type of device, its layout, or the involved transport mechanisms. For two‐terminal devices, where charge and heat currents flow along the same path, we find a particularly simple and intuitive expression for the figure of merit ZT. In multi‐terminal devices with different paths for the currents, the thermoelectric efficiency does not admit such a simple interpretation. Nonetheless, nontrivial device‐independent statements can be made about the efficiency. As a practical example, we consider the heat‐to‐current converter Sánchez and Büttiker, Phys. Rev. B 83, 085428 (2011).}, author = {Eltschka, Christopher and Thierschmann, Holger and Buhmann, Hartmut and Siewert, Jens}, journal = {physica status solidi (a)}, keywords = {qt}, month = 12, number = 3, pages = {626–634}, publisher = {Wiley}, title = {Thermoelectric efficiency in the linear transport regime}, volume = 213, year = 2015 }

%0 Journal Article %1 eltschka2015thermoelectric %A Eltschka, Christopher %A Thierschmann, Holger %A Buhmann, Hartmut %A Siewert, Jens %D 2015 %I Wiley %J physica status solidi (a) %N 3 %P 626--634 %R 10.1002/pssa.201532612 %T Thermoelectric efficiency in the linear transport regime %V 213 %X Improving the efficiency of thermoelectric devices is a long‐term goal in thermoelectricity research. Deeper insight into the meaning of the related quantities, in particular the figure of merit is instrumental for progress in this direction. Here, we study the regime of linear transport where entirely general statements can be made for the electronic part of the thermoelectric efficiency. These results essentially do not depend on the type of device, its layout, or the involved transport mechanisms. For two‐terminal devices, where charge and heat currents flow along the same path, we find a particularly simple and intuitive expression for the figure of merit ZT. In multi‐terminal devices with different paths for the currents, the thermoelectric efficiency does not admit such a simple interpretation. Nonetheless, nontrivial device‐independent statements can be made about the efficiency. As a practical example, we consider the heat‐to‐current converter Sánchez and Büttiker, Phys. Rev. B 83, 085428 (2011).
Thermal gating of charge currents with Coulomb coupled quantum dots. Thierschmann, H; Arnold, F; Mittermüller, M; Maier, L; Heyn, C; Hansen, W; Buhmann, H; Molenkamp, L W. In New Journal of Physics, 17, p. 113003. 2015.
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We have observed thermal gating, i.e. electrostatic gating induced by hot electrons. The effect occurs in a device consisting of two capacitively coupled quantum dots. The double dot system is coupled to a hot electron reservoir on one side (QD1), while the conductance of the second dot (QD2) is monitored. When a bias across QD2 is applied we observe a current which is strongly dependent on the temperature of the heat reservoir. This current can be either enhanced or suppressed, depending on the relative energetic alignment of the QD levels. Thus, the system can be used to control a charge current by hot electrons.

@article{thierschmann2015thermal, abstract = {We have observed thermal gating, i.e. electrostatic gating induced by hot electrons. The effect occurs in a device consisting of two capacitively coupled quantum dots. The double dot system is coupled to a hot electron reservoir on one side (QD1), while the conductance of the second dot (QD2) is monitored. When a bias across QD2 is applied we observe a current which is strongly dependent on the temperature of the heat reservoir. This current can be either enhanced or suppressed, depending on the relative energetic alignment of the QD levels. Thus, the system can be used to control a charge current by hot electrons.}, author = {Thierschmann, H and Arnold, F and Mittermüller, M and Maier, L and Heyn, C and Hansen, W and Buhmann, H and Molenkamp, L W}, journal = {New Journal of Physics}, keywords = {qt}, month = 11, pages = 113003, title = {Thermal gating of charge currents with Coulomb coupled quantum dots}, volume = 17, year = 2015 }

%0 Journal Article %1 thierschmann2015thermal %A Thierschmann, H %A Arnold, F %A Mittermüller, M %A Maier, L %A Heyn, C %A Hansen, W %A Buhmann, H %A Molenkamp, L W %D 2015 %J New Journal of Physics %P 113003 %R 10.1088/1367-2630/17/11/113003 %T Thermal gating of charge currents with Coulomb coupled quantum dots %V 17 %X We have observed thermal gating, i.e. electrostatic gating induced by hot electrons. The effect occurs in a device consisting of two capacitively coupled quantum dots. The double dot system is coupled to a hot electron reservoir on one side (QD1), while the conductance of the second dot (QD2) is monitored. When a bias across QD2 is applied we observe a current which is strongly dependent on the temperature of the heat reservoir. This current can be either enhanced or suppressed, depending on the relative energetic alignment of the QD levels. Thus, the system can be used to control a charge current by hot electrons.
Rashba Effect and Beating Patterns in the THz Magneto-Photoresponse of a HgTe-Based Two-Dimensional Electron Gas. Pakmehr, M.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; McCombe, B. D. In Selected Topics in Electronics and Systems, 56, pp. 67–73. 2015.
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HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magneto-photoresponse (PR) and magneto-transport measurements. The QW sample has the conventional band alignment with the well thickness (6.1 nm) slightly smaller than the critical thickness for the topological phase transition. The effective gap of this structure is roughly 10 meV, and the large sheet density (nS ≈ 1.5 × 10^16 m^−2) of the two-dimensional electron gas (2DEG) results in a very large Fermi energy (EF ~ 160 meV). We have found several interesting effects at these high densities. In this paper we focus on an observed beating of quantum oscillations in the PR signal (at 1.83 THz) and compare it with direct measurements of oscillations in the longitudinal magneto-resistance (Rxx) The mechanism for the PR is cyclotron resonance absorption heating of the electrons (an electron bolometric effect). We attribute the beating to Rashba splitting of the spin states, which is barely observable in direct Rxx measurements under strong gate-induced electric fields.

@article{pakmehr2015rashba, abstract = {HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magneto-photoresponse (PR) and magneto-transport measurements. The QW sample has the conventional band alignment with the well thickness (6.1 nm) slightly smaller than the critical thickness for the topological phase transition. The effective gap of this structure is roughly 10 meV, and the large sheet density (nS ≈ 1.5 × 10^16 m^−2) of the two-dimensional electron gas (2DEG) results in a very large Fermi energy (EF 160 meV). We have found several interesting effects at these high densities. In this paper we focus on an observed beating of quantum oscillations in the PR signal (at 1.83 THz) and compare it with direct measurements of oscillations in the longitudinal magneto-resistance (Rxx) The mechanism for the PR is cyclotron resonance absorption heating of the electrons (an electron bolometric effect). We attribute the beating to Rashba splitting of the spin states, which is barely observable in direct Rxx measurements under strong gate-induced electric fields.}, author = {Pakmehr, M. and Brüne, C. and Buhmann, H. and Molenkamp, L. W. and McCombe, B. D.}, journal = {Selected Topics in Electronics and Systems}, keywords = {qt}, month = {09}, pages = {67-73}, title = {Rashba Effect and Beating Patterns in the THz Magneto-Photoresponse of a HgTe-Based Two-Dimensional Electron Gas}, volume = 56, year = 2015 }

%0 Journal Article %1 pakmehr2015rashba %A Pakmehr, M. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %A McCombe, B. D. %D 2015 %J Selected Topics in Electronics and Systems %P 67-73 %R 10.1142/9789814725200_0005 %T Rashba Effect and Beating Patterns in the THz Magneto-Photoresponse of a HgTe-Based Two-Dimensional Electron Gas %V 56 %X HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magneto-photoresponse (PR) and magneto-transport measurements. The QW sample has the conventional band alignment with the well thickness (6.1 nm) slightly smaller than the critical thickness for the topological phase transition. The effective gap of this structure is roughly 10 meV, and the large sheet density (nS ≈ 1.5 × 10^16 m^−2) of the two-dimensional electron gas (2DEG) results in a very large Fermi energy (EF ~ 160 meV). We have found several interesting effects at these high densities. In this paper we focus on an observed beating of quantum oscillations in the PR signal (at 1.83 THz) and compare it with direct measurements of oscillations in the longitudinal magneto-resistance (Rxx) The mechanism for the PR is cyclotron resonance absorption heating of the electrons (an electron bolometric effect). We attribute the beating to Rashba splitting of the spin states, which is barely observable in direct Rxx measurements under strong gate-induced electric fields. %@ 978-981-4725-19-4
Phase-sensitive {SQUIDs} based on the 3D topological insulator {HgTe}. Maier, L; Bocquillon, E; Grimm, M; Oostinga, J B; Ames, C; Gould, C; Brüne, C; Buhmann, H; Molenkamp, L W. In Physica Scripta, T164, p. 014002. {IOP} Publishing, 2015.
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Three-dimensional (3D) topological insulators represent a new class of materials in which transport is governed by Dirac surface states while the bulk remains insulating. Due to helical spin polarization of the surface states, the coupling of a 3D topological insulator to a nearby superconductor is expected to generate unconventional proximity induced p-wave superconductivity. We report here on the development and measurements of superconducting quantum interference devices on the surface of strained HgTe, a 3D topological insulator, as a potential tool to investigate this effect.

@article{maier2015phasesensitive, abstract = {Three-dimensional (3D) topological insulators represent a new class of materials in which transport is governed by Dirac surface states while the bulk remains insulating. Due to helical spin polarization of the surface states, the coupling of a 3D topological insulator to a nearby superconductor is expected to generate unconventional proximity induced p-wave superconductivity. We report here on the development and measurements of superconducting quantum interference devices on the surface of strained HgTe, a 3D topological insulator, as a potential tool to investigate this effect.}, author = {Maier, L and Bocquillon, E and Grimm, M and Oostinga, J B and Ames, C and Gould, C and Brüne, C and Buhmann, H and Molenkamp, L W}, journal = {Physica Scripta}, keywords = {qt}, month = {08}, pages = {014002}, publisher = {{IOP} Publishing}, title = {Phase-sensitive {SQUIDs} based on the 3D topological insulator {HgTe}}, volume = {T164}, year = 2015 }

%0 Journal Article %1 maier2015phasesensitive %A Maier, L %A Bocquillon, E %A Grimm, M %A Oostinga, J B %A Ames, C %A Gould, C %A Brüne, C %A Buhmann, H %A Molenkamp, L W %D 2015 %I {IOP} Publishing %J Physica Scripta %P 014002 %R 10.1088/0031-8949/2015/t164/014002 %T Phase-sensitive {SQUIDs} based on the 3D topological insulator {HgTe} %V T164 %X Three-dimensional (3D) topological insulators represent a new class of materials in which transport is governed by Dirac surface states while the bulk remains insulating. Due to helical spin polarization of the surface states, the coupling of a 3D topological insulator to a nearby superconductor is expected to generate unconventional proximity induced p-wave superconductivity. We report here on the development and measurements of superconducting quantum interference devices on the surface of strained HgTe, a 3D topological insulator, as a potential tool to investigate this effect.
Observation of Thermoelectric Voltages from the Two-Dimensional Electron Gas of a HgTe Quantum Well Due to Resonant THz Laser Heating. Pakmehr, Mehdi; McCombe, B. D.; Bruene, C.; Buhmann, H.; Molenkamp, L. W. In Journal of Electronic Materials, 44(10), pp. 3598–3602. 2015.
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HgTe quantum wells (QWs) have shown a number of interesting phenomena, recently the first two-dimensional topological insulating state. We have studied thermoelectric photovoltages of two-dimensional electrons in a 6.1 nm wide HgTe QW induced by cyclotron resonance absorption (B = 2 to 5 T) of a THz laser beam. We have estimated thermopower coefficients by detailed analysis of the photovoltage signals developed across various contacts of a large Hall bar structure at a bath temperature of 1.6 K. The photovoltage signals are washed out at bath temperature of 18 K.

@article{pakmehr2015observation, abstract = {HgTe quantum wells (QWs) have shown a number of interesting phenomena, recently the first two-dimensional topological insulating state. We have studied thermoelectric photovoltages of two-dimensional electrons in a 6.1 nm wide HgTe QW induced by cyclotron resonance absorption (B = 2 to 5 T) of a THz laser beam. We have estimated thermopower coefficients by detailed analysis of the photovoltage signals developed across various contacts of a large Hall bar structure at a bath temperature of 1.6 K. The photovoltage signals are washed out at bath temperature of 18 K.}, author = {Pakmehr, Mehdi and McCombe, B. D. and Bruene, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Journal of Electronic Materials}, keywords = {qt}, month = {08}, number = 10, pages = {3598–3602}, title = {Observation of Thermoelectric Voltages from the Two-Dimensional Electron Gas of a HgTe Quantum Well Due to Resonant THz Laser Heating}, volume = 44, year = 2015 }

%0 Journal Article %1 pakmehr2015observation %A Pakmehr, Mehdi %A McCombe, B. D. %A Bruene, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2015 %J Journal of Electronic Materials %N 10 %P 3598--3602 %R 10.1007/s11664-015-3883-5 %T Observation of Thermoelectric Voltages from the Two-Dimensional Electron Gas of a HgTe Quantum Well Due to Resonant THz Laser Heating %V 44 %X HgTe quantum wells (QWs) have shown a number of interesting phenomena, recently the first two-dimensional topological insulating state. We have studied thermoelectric photovoltages of two-dimensional electrons in a 6.1 nm wide HgTe QW induced by cyclotron resonance absorption (B = 2 to 5 T) of a THz laser beam. We have estimated thermopower coefficients by detailed analysis of the photovoltage signals developed across various contacts of a large Hall bar structure at a bath temperature of 1.6 K. The photovoltage signals are washed out at bath temperature of 18 K.
Three-terminal energy harvester with coupled quantum dots. Thierschmann, Holger; S{{á}}nchez, Rafael; Sothmann, Björn; Arnold, Fabian; Heyn, Christian; Hansen, Wolfgang; Buhmann, Hartmut; Molenkamp, Laurens W. In Nature Nanotechnology, 10(10), pp. 854–858. Springer Science and Business Media {LLC}, 2015.
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Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines.

@article{thierschmann2015threeterminal, abstract = {Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines.}, author = {Thierschmann, Holger and S{\'{a}}nchez, Rafael and Sothmann, Björn and Arnold, Fabian and Heyn, Christian and Hansen, Wolfgang and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Nature Nanotechnology}, keywords = {qt}, month = {08}, number = 10, pages = {854–858}, publisher = {Springer Science and Business Media {LLC}}, title = {Three-terminal energy harvester with coupled quantum dots}, volume = 10, year = 2015 }

%0 Journal Article %1 thierschmann2015threeterminal %A Thierschmann, Holger %A S{{á}}nchez, Rafael %A Sothmann, Björn %A Arnold, Fabian %A Heyn, Christian %A Hansen, Wolfgang %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2015 %I Springer Science and Business Media {LLC} %J Nature Nanotechnology %N 10 %P 854--858 %R 10.1038/nnano.2015.176 %T Three-terminal energy harvester with coupled quantum dots %V 10 %X Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines.
Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry. Ma, Eric Yue; Calvo, M. Reyes; Wang, Jing; Lian, Biao; Mühlbauer, Mathias; Brüne, Christoph; Cui, Yong-Tao; Lai, Keji; Kundhikanjana, Worasom; Yang, Yongliang; Baenninger, Matthias; König, Markus; Ames, Christopher; Buhmann, Hartmut; Leubner, Philipp; Molenkamp, Laurens W.; Zhang, Shou-Cheng; Goldhaber-Gordon, David; Kelly, Michael A.; Shen, Zhi-Xun. In Nature Communications, 6(1). Springer Science and Business Media {LLC}, 2015.
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The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.

@article{ma2015unexpected, abstract = {The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.}, author = {Ma, Eric Yue and Calvo, M. Reyes and Wang, Jing and Lian, Biao and Mühlbauer, Mathias and Brüne, Christoph and Cui, Yong-Tao and Lai, Keji and Kundhikanjana, Worasom and Yang, Yongliang and Baenninger, Matthias and König, Markus and Ames, Christopher and Buhmann, Hartmut and Leubner, Philipp and Molenkamp, Laurens W. and Zhang, Shou-Cheng and Goldhaber-Gordon, David and Kelly, Michael A. and Shen, Zhi-Xun}, journal = {Nature Communications}, keywords = {qt}, month = {05}, number = 1, publisher = {Springer Science and Business Media {LLC}}, title = {Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry}, volume = 6, year = 2015 }

%0 Journal Article %1 ma2015unexpected %A Ma, Eric Yue %A Calvo, M. Reyes %A Wang, Jing %A Lian, Biao %A Mühlbauer, Mathias %A Brüne, Christoph %A Cui, Yong-Tao %A Lai, Keji %A Kundhikanjana, Worasom %A Yang, Yongliang %A Baenninger, Matthias %A König, Markus %A Ames, Christopher %A Buhmann, Hartmut %A Leubner, Philipp %A Molenkamp, Laurens W. %A Zhang, Shou-Cheng %A Goldhaber-Gordon, David %A Kelly, Michael A. %A Shen, Zhi-Xun %D 2015 %I Springer Science and Business Media {LLC} %J Nature Communications %N 1 %R 10.1038/ncomms8252 %T Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry %V 6 %X The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.
Temperature-driven transition from a semiconductor to a topological insulator. Wiedmann, Steffen; Jost, Andreas; Thienel, Cornelius; Brüne, Christoph; Leubner, Philipp; Buhmann, Hartmut; Molenkamp, Laurens W.; Maan, J. C.; Zeitler, Uli. In Phys. Rev. B, 91(20), p. 205311. American Physical Society, 2015.
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We report on a temperature-induced transition from a conventional semiconductor to a two-dimensional topological insulator investigated by means of magnetotransport experiments on HgTe/CdTe quantum well structures. At low temperatures, we are in the regime of the quantum spin Hall effect and observe an ambipolar quantized Hall resistance by tuning the Fermi energy through the bulk band gap. At room temperature, we find electron and hole conduction that can be described by a classical two-carrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic low-field magnetoresistance if electrons and holes coexist. Temperature-dependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.

@article{wiedmann2015temperaturedriven, abstract = {We report on a temperature-induced transition from a conventional semiconductor to a two-dimensional topological insulator investigated by means of magnetotransport experiments on HgTe/CdTe quantum well structures. At low temperatures, we are in the regime of the quantum spin Hall effect and observe an ambipolar quantized Hall resistance by tuning the Fermi energy through the bulk band gap. At room temperature, we find electron and hole conduction that can be described by a classical two-carrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic low-field magnetoresistance if electrons and holes coexist. Temperature-dependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.}, author = {Wiedmann, Steffen and Jost, Andreas and Thienel, Cornelius and Br\"une, Christoph and Leubner, Philipp and Buhmann, Hartmut and Molenkamp, Laurens W. and Maan, J. C. and Zeitler, Uli}, journal = {Phys. Rev. B}, keywords = {qt}, month = {05}, number = 20, pages = 205311, publisher = {American Physical Society}, title = {Temperature-driven transition from a semiconductor to a topological insulator}, volume = 91, year = 2015 }

%0 Journal Article %1 wiedmann2015temperaturedriven %A Wiedmann, Steffen %A Jost, Andreas %A Thienel, Cornelius %A Brüne, Christoph %A Leubner, Philipp %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Maan, J. C. %A Zeitler, Uli %D 2015 %I American Physical Society %J Phys. Rev. B %N 20 %P 205311 %R 10.1103/PhysRevB.91.205311 %T Temperature-driven transition from a semiconductor to a topological insulator %V 91 %X We report on a temperature-induced transition from a conventional semiconductor to a two-dimensional topological insulator investigated by means of magnetotransport experiments on HgTe/CdTe quantum well structures. At low temperatures, we are in the regime of the quantum spin Hall effect and observe an ambipolar quantized Hall resistance by tuning the Fermi energy through the bulk band gap. At room temperature, we find electron and hole conduction that can be described by a classical two-carrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic low-field magnetoresistance if electrons and holes coexist. Temperature-dependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.
Nonsinusoidal Current-Phase Relationship in Josephson Junctions from the 3D Topological Insulator HgTe. Sochnikov, Ilya; Maier, Luis; Watson, Christopher A.; Kirtley, John R.; Gould, Charles; Tkachov, Grigory; Hankiewicz, Ewelina M.; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Moler, Kathryn A. In Phys. Rev. Lett., 114(6), p. 066801. American Physical Society, 2015.
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We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.

@article{sochnikov2015nonsinusoidal, abstract = {We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.}, author = {Sochnikov, Ilya and Maier, Luis and Watson, Christopher A. and Kirtley, John R. and Gould, Charles and Tkachov, Grigory and Hankiewicz, Ewelina M. and Br\"une, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Moler, Kathryn A.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {02}, number = 6, pages = {066801}, publisher = {American Physical Society}, title = {Nonsinusoidal Current-Phase Relationship in Josephson Junctions from the 3D Topological Insulator HgTe}, volume = 114, year = 2015 }

%0 Journal Article %1 sochnikov2015nonsinusoidal %A Sochnikov, Ilya %A Maier, Luis %A Watson, Christopher A. %A Kirtley, John R. %A Gould, Charles %A Tkachov, Grigory %A Hankiewicz, Ewelina M. %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Moler, Kathryn A. %D 2015 %I American Physical Society %J Phys. Rev. Lett. %N 6 %P 066801 %R 10.1103/PhysRevLett.114.066801 %T Nonsinusoidal Current-Phase Relationship in Josephson Junctions from the 3D Topological Insulator HgTe %V 114 %X We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.

Landau levels and spin splitting in the two-dimensional electron gas of a HgTe quantum well near the critical width for the topological phase transition. Pakmehr, M.; Bruene, C.; Buhmann, H.; Molenkamp, L. W.; Stier, A. V.; McCombe, B. D. In Phys. Rev. B, 90(23), p. 235414. American Physical Society, 2014.
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We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with Hg0.3Cd0.7Te barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (Rxx and Rxy) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the “bulk” quasi-2D Landau-level (LL) spectrum of the conduction band at high energies (≈135−160meV) above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed (Espin>Ecyclotron) require a significantly larger g-parameter ge for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ge also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the Rxx measurements at lower electron densities (Fermi energies) produced by negative gate bias.

@article{pakmehr2014landau, abstract = {We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with Hg0.3Cd0.7Te barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (Rxx and Rxy) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the “bulk” quasi-2D Landau-level (LL) spectrum of the conduction band at high energies (≈135−160meV) above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed (Espin>Ecyclotron) require a significantly larger g-parameter ge for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ge also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the Rxx measurements at lower electron densities (Fermi energies) produced by negative gate bias.}, author = {Pakmehr, M. and Bruene, C. and Buhmann, H. and Molenkamp, L. W. and Stier, A. V. and McCombe, B. D.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 12, number = 23, pages = 235414, publisher = {American Physical Society}, title = {Landau levels and spin splitting in the two-dimensional electron gas of a HgTe quantum well near the critical width for the topological phase transition}, volume = 90, year = 2014 }

%0 Journal Article %1 pakmehr2014landau %A Pakmehr, M. %A Bruene, C. %A Buhmann, H. %A Molenkamp, L. W. %A Stier, A. V. %A McCombe, B. D. %D 2014 %I American Physical Society %J Phys. Rev. B %N 23 %P 235414 %R 10.1103/PhysRevB.90.235414 %T Landau levels and spin splitting in the two-dimensional electron gas of a HgTe quantum well near the critical width for the topological phase transition %V 90 %X We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with Hg0.3Cd0.7Te barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (Rxx and Rxy) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the “bulk” quasi-2D Landau-level (LL) spectrum of the conduction band at high energies (≈135−160meV) above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed (Espin>Ecyclotron) require a significantly larger g-parameter ge for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ge also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the Rxx measurements at lower electron densities (Fermi energies) produced by negative gate bias.
Dirac-Screening Stabilized Surface-State Transport in a Topological Insulator. Brüne, Christoph; Thienel, Cornelius; Stuiber, Michael; Böttcher, Jan; Buhmann, Hartmut; Novik, Elena G.; Liu, Chao-Xing; Hankiewicz, Ewelina M.; Molenkamp, Laurens W. In Phys. Rev. X, 4(4), p. 041045. American Physical Society, 2014.
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We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×10^11 cm^−2<n<2×10^12 cm^−2). These observations imply that even at large carrier densities, the transport is surface-state dominated, where bulk transport would have been expected to coexist already. Moreover, the density dependence of the Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A k⋅p model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.

@article{brune2014diracscreening, abstract = {We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×10^11 cm^−2<n<2×10^12 cm^−2). These observations imply that even at large carrier densities, the transport is surface-state dominated, where bulk transport would have been expected to coexist already. Moreover, the density dependence of the Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A k⋅p model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.}, author = {Br\"une, Christoph and Thienel, Cornelius and Stuiber, Michael and B\"ottcher, Jan and Buhmann, Hartmut and Novik, Elena G. and Liu, Chao-Xing and Hankiewicz, Ewelina M. and Molenkamp, Laurens W.}, journal = {Phys. Rev. X}, keywords = {qt}, month = 12, number = 4, pages = {041045}, publisher = {American Physical Society}, title = {Dirac-Screening Stabilized Surface-State Transport in a Topological Insulator}, volume = 4, year = 2014 }

%0 Journal Article %1 brune2014diracscreening %A Brüne, Christoph %A Thienel, Cornelius %A Stuiber, Michael %A Böttcher, Jan %A Buhmann, Hartmut %A Novik, Elena G. %A Liu, Chao-Xing %A Hankiewicz, Ewelina M. %A Molenkamp, Laurens W. %D 2014 %I American Physical Society %J Phys. Rev. X %N 4 %P 041045 %R 10.1103/PhysRevX.4.041045 %T Dirac-Screening Stabilized Surface-State Transport in a Topological Insulator %V 4 %X We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×10^11 cm^−2<n<2×10^12 cm^−2). These observations imply that even at large carrier densities, the transport is surface-state dominated, where bulk transport would have been expected to coexist already. Moreover, the density dependence of the Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A k⋅p model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.
Induced superconductivity in the quantum spin Hall edge. Hart, Sean; Ren, Hechen; Wagner, Timo; Leubner, Philipp; Mühlbauer, Mathias; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Yacoby, Amir. In Nature Physics, 10(9), pp. 638–643. Springer Science and Business Media {LLC}, 2014.
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Topological insulators are a newly discovered phase of matter characterized by gapped bulk states surrounded by conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer6. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material that becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. Our results provide evidence for supercurrents induced in the helical edges of the quantum spin Hall effect, establishing this system as a promising avenue towards topological superconductivity. In addition to directly confirming the existence of the topological edge channels, our results also provide a measurement of their widths, which range from 180 nm to 408 nm.

@article{hart2014induced, abstract = {Topological insulators are a newly discovered phase of matter characterized by gapped bulk states surrounded by conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer6. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material that becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. Our results provide evidence for supercurrents induced in the helical edges of the quantum spin Hall effect, establishing this system as a promising avenue towards topological superconductivity. In addition to directly confirming the existence of the topological edge channels, our results also provide a measurement of their widths, which range from 180 nm to 408 nm.}, author = {Hart, Sean and Ren, Hechen and Wagner, Timo and Leubner, Philipp and Mühlbauer, Mathias and Brüne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Yacoby, Amir}, journal = {Nature Physics}, keywords = {qt}, month = {08}, number = 9, pages = {638–643}, publisher = {Springer Science and Business Media {LLC}}, title = {Induced superconductivity in the quantum spin Hall edge}, volume = 10, year = 2014 }

%0 Journal Article %1 hart2014induced %A Hart, Sean %A Ren, Hechen %A Wagner, Timo %A Leubner, Philipp %A Mühlbauer, Mathias %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Yacoby, Amir %D 2014 %I Springer Science and Business Media {LLC} %J Nature Physics %N 9 %P 638--643 %R 10.1038/nphys3036 %T Induced superconductivity in the quantum spin Hall edge %V 10 %X Topological insulators are a newly discovered phase of matter characterized by gapped bulk states surrounded by conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer6. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal. Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material that becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. Our results provide evidence for supercurrents induced in the helical edges of the quantum spin Hall effect, establishing this system as a promising avenue towards topological superconductivity. In addition to directly confirming the existence of the topological edge channels, our results also provide a measurement of their widths, which range from 180 nm to 408 nm.
Suppressing Twin Formation in Bi2Se3Thin Films. Tarakina, N. V.; Schreyeck, S.; Luysberg, M.; Grauer, S.; Schumacher, C.; Karczewski, G.; Brunner, K.; Gould, C.; Buhmann, H.; Dunin-Borkowski, R. E.; Molenkamp, L. W. In Advanced Materials Interfaces, 1(5), p. 1400134. Wiley, 2014.
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The microstructure of Bi2Se3 topological‐insulator thin films grown by molecular beam epitaxy on InP(111)A and InP(111)B substrates that have different surface roughnesses has been studied in detail using X‐ray diffraction, X‐ray reflectivity, atomic force microscopy and probe‐corrected scanning transmission electron microscopy. The use of a rough Fe‐doped InP(111)B substrate results in complete suppression of twin formation in the Bi2Se3 thin films and a perfect interface between the films and their substrates. The only type of structural defect that persists in the twin‐free films is an antiphase domain boundary, which is associated with variations in substrate height. We also show that the substrate surface termination influences which family of twin domains dominates.

@article{tarakina2014suppressing, abstract = {The microstructure of Bi2Se3 topological‐insulator thin films grown by molecular beam epitaxy on InP(111)A and InP(111)B substrates that have different surface roughnesses has been studied in detail using X‐ray diffraction, X‐ray reflectivity, atomic force microscopy and probe‐corrected scanning transmission electron microscopy. The use of a rough Fe‐doped InP(111)B substrate results in complete suppression of twin formation in the Bi2Se3 thin films and a perfect interface between the films and their substrates. The only type of structural defect that persists in the twin‐free films is an antiphase domain boundary, which is associated with variations in substrate height. We also show that the substrate surface termination influences which family of twin domains dominates.}, author = {Tarakina, N. V. and Schreyeck, S. and Luysberg, M. and Grauer, S. and Schumacher, C. and Karczewski, G. and Brunner, K. and Gould, C. and Buhmann, H. and Dunin-Borkowski, R. E. and Molenkamp, L. W.}, journal = {Advanced Materials Interfaces}, keywords = {qt}, month = {05}, number = 5, pages = 1400134, publisher = {Wiley}, title = {Suppressing Twin Formation in Bi2Se3Thin Films}, volume = 1, year = 2014 }

%0 Journal Article %1 tarakina2014suppressing %A Tarakina, N. V. %A Schreyeck, S. %A Luysberg, M. %A Grauer, S. %A Schumacher, C. %A Karczewski, G. %A Brunner, K. %A Gould, C. %A Buhmann, H. %A Dunin-Borkowski, R. E. %A Molenkamp, L. W. %D 2014 %I Wiley %J Advanced Materials Interfaces %N 5 %P 1400134 %R 10.1002/admi.201400134 %T Suppressing Twin Formation in Bi2Se3Thin Films %V 1 %X The microstructure of Bi2Se3 topological‐insulator thin films grown by molecular beam epitaxy on InP(111)A and InP(111)B substrates that have different surface roughnesses has been studied in detail using X‐ray diffraction, X‐ray reflectivity, atomic force microscopy and probe‐corrected scanning transmission electron microscopy. The use of a rough Fe‐doped InP(111)B substrate results in complete suppression of twin formation in the Bi2Se3 thin films and a perfect interface between the films and their substrates. The only type of structural defect that persists in the twin‐free films is an antiphase domain boundary, which is associated with variations in substrate height. We also show that the substrate surface termination influences which family of twin domains dominates.
One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires. Mühlbauer, M.; Budewitz, A.; Büttner, B.; Tkachov, G.; Hankiewicz, E. M.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Lett., 112(14), p. 146803. American Physical Society, 2014.
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We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.

@article{muhlbauer2014onedimensional, abstract = {We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.}, author = {M\"uhlbauer, M. and Budewitz, A. and B\"uttner, B. and Tkachov, G. and Hankiewicz, E. M. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {04}, number = 14, pages = 146803, publisher = {American Physical Society}, title = {One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires}, volume = 112, year = 2014 }

%0 Journal Article %1 muhlbauer2014onedimensional %A Mühlbauer, M. %A Budewitz, A. %A Büttner, B. %A Tkachov, G. %A Hankiewicz, E. M. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2014 %I American Physical Society %J Phys. Rev. Lett. %N 14 %P 146803 %R 10.1103/PhysRevLett.112.146803 %T One-Dimensional Weak Antilocalization Due to the Berry Phase in HgTe Wires %V 112 %X We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.
Spin Texture of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ Thin Films in the Quantum Tunneling Limit. Landolt, Gabriel; Schreyeck, Steffen; Eremeev, Sergey V.; Slomski, Bartosz; Muff, Stefan; Osterwalder, Jürg; Chulkov, Evgueni V.; Gould, Charles; Karczewski, Grzegorz; Brunner, Karl; Buhmann, Hartmut; Molenkamp, Laurens W.; Dil, J. Hugo. In Phys. Rev. Lett., 112(5), p. 057601. American Physical Society, 2014.
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By means of spin- and angle-resolved photoelectron spectroscopy we studied the spin structure of thin films of the topological insulator Bi2Se3 grown on InP(111). For thicknesses below six quintuple layers the spin-polarized metallic topological surface states interact with each other via quantum tunneling and a gap opens. Our measurements show that the resulting surface states can be described by massive Dirac cones which are split in a Rashba-like manner due to the substrate induced inversion asymmetry. The inner and the outer Rashba branches have distinct localization in the top and the bottom part of the film, whereas the band apices are delocalized throughout the entire film. Supported by ab initio calculations, our observations help in the understanding of the evolution of the surface states at the topological phase transition and provide the groundwork for the realization of two-dimensional spintronic devices based on topological semiconductors.

@article{landolt2014texture, abstract = {By means of spin- and angle-resolved photoelectron spectroscopy we studied the spin structure of thin films of the topological insulator Bi2Se3 grown on InP(111). For thicknesses below six quintuple layers the spin-polarized metallic topological surface states interact with each other via quantum tunneling and a gap opens. Our measurements show that the resulting surface states can be described by massive Dirac cones which are split in a Rashba-like manner due to the substrate induced inversion asymmetry. The inner and the outer Rashba branches have distinct localization in the top and the bottom part of the film, whereas the band apices are delocalized throughout the entire film. Supported by ab initio calculations, our observations help in the understanding of the evolution of the surface states at the topological phase transition and provide the groundwork for the realization of two-dimensional spintronic devices based on topological semiconductors.}, author = {Landolt, Gabriel and Schreyeck, Steffen and Eremeev, Sergey V. and Slomski, Bartosz and Muff, Stefan and Osterwalder, J\"urg and Chulkov, Evgueni V. and Gould, Charles and Karczewski, Grzegorz and Brunner, Karl and Buhmann, Hartmut and Molenkamp, Laurens W. and Dil, J. Hugo}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {02}, number = 5, pages = {057601}, publisher = {American Physical Society}, title = {Spin Texture of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ Thin Films in the Quantum Tunneling Limit}, volume = 112, year = 2014 }

%0 Journal Article %1 landolt2014texture %A Landolt, Gabriel %A Schreyeck, Steffen %A Eremeev, Sergey V. %A Slomski, Bartosz %A Muff, Stefan %A Osterwalder, Jürg %A Chulkov, Evgueni V. %A Gould, Charles %A Karczewski, Grzegorz %A Brunner, Karl %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Dil, J. Hugo %D 2014 %I American Physical Society %J Phys. Rev. Lett. %N 5 %P 057601 %R 10.1103/PhysRevLett.112.057601 %T Spin Texture of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ Thin Films in the Quantum Tunneling Limit %V 112 %X By means of spin- and angle-resolved photoelectron spectroscopy we studied the spin structure of thin films of the topological insulator Bi2Se3 grown on InP(111). For thicknesses below six quintuple layers the spin-polarized metallic topological surface states interact with each other via quantum tunneling and a gap opens. Our measurements show that the resulting surface states can be described by massive Dirac cones which are split in a Rashba-like manner due to the substrate induced inversion asymmetry. The inner and the outer Rashba branches have distinct localization in the top and the bottom part of the film, whereas the band apices are delocalized throughout the entire film. Supported by ab initio calculations, our observations help in the understanding of the evolution of the surface states at the topological phase transition and provide the groundwork for the realization of two-dimensional spintronic devices based on topological semiconductors.

Diffusion thermopower of a serial double quantum dot. Thierschmann, H; Henke, M; Knorr, J; Maier, L; Heyn, C; Hansen, W; Buhmann, H; Molenkamp, L W. In New Journal of Physics, 15, p. 123010. 2013.
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We have experimentally studied the diffusion thermopower of a serial double quantum dot, defined electrostatically in a GaAs/AlGaAs heterostructure. We present the thermopower stability diagram for a temperature difference ΔT = (20 ± 10) mK across the device and find a maximum thermovoltage signal of several μV in the vicinity of the triple points. Along a constant energy axis in this regime, the data show a characteristic pattern which is in agreement with Mott's relation and can be well understood within a model of sequential transport.

@article{thierschmann2013diffusion, abstract = {We have experimentally studied the diffusion thermopower of a serial double quantum dot, defined electrostatically in a GaAs/AlGaAs heterostructure. We present the thermopower stability diagram for a temperature difference ΔT = (20 ± 10) mK across the device and find a maximum thermovoltage signal of several μV in the vicinity of the triple points. Along a constant energy axis in this regime, the data show a characteristic pattern which is in agreement with Mott's relation and can be well understood within a model of sequential transport.}, author = {Thierschmann, H and Henke, M and Knorr, J and Maier, L and Heyn, C and Hansen, W and Buhmann, H and Molenkamp, L W}, journal = {New Journal of Physics}, keywords = {qt}, month = 12, pages = 123010, title = {Diffusion thermopower of a serial double quantum dot}, volume = 15, year = 2013 }

%0 Journal Article %1 thierschmann2013diffusion %A Thierschmann, H %A Henke, M %A Knorr, J %A Maier, L %A Heyn, C %A Hansen, W %A Buhmann, H %A Molenkamp, L W %D 2013 %J New Journal of Physics %P 123010 %R 10.1088/1367-2630/15/12/123010 %T Diffusion thermopower of a serial double quantum dot %V 15 %X We have experimentally studied the diffusion thermopower of a serial double quantum dot, defined electrostatically in a GaAs/AlGaAs heterostructure. We present the thermopower stability diagram for a temperature difference ΔT = (20 ± 10) mK across the device and find a maximum thermovoltage signal of several μV in the vicinity of the triple points. Along a constant energy axis in this regime, the data show a characteristic pattern which is in agreement with Mott's relation and can be well understood within a model of sequential transport.
Quantum Spin Hall State in HgTe. Brüne, C; Buhmann, H; Molenkamp, L W. In Contemporary Concepts of Condensed Matter Science, 6, pp. 125–142. 2013.
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This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.

@article{brune2013quantum, abstract = {This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.}, author = {Brüne, C and Buhmann, H and Molenkamp, L W}, journal = {Contemporary Concepts of Condensed Matter Science}, keywords = {qt}, month = 11, pages = {125-142}, title = {Quantum Spin Hall State in HgTe}, volume = 6, year = 2013 }

%0 Journal Article %1 brune2013quantum %A Brüne, C %A Buhmann, H %A Molenkamp, L W %D 2013 %J Contemporary Concepts of Condensed Matter Science %P 125-142 %R 10.1016/B978-0-444-63314-9.00005-6 %T Quantum Spin Hall State in HgTe %V 6 %X This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.
Room temperature electrically tunable terahertz Faraday effect. Shuvaev, A; Pimenov, A; Astakhov, G. V.; Mühlbauer, M; Brüne, C; Buhmann, H; Molenkamp, L. W. In Appl. Phys. Lett., 102(24), p. 241902-. American Institute of Physics, 2013.
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We demonstrate electrical control of the room temperature Faraday effect in a 100-nm-thick film of strained HgTe, which is a topological insulator. The terahertz (THz) response of our device is dominated by the Drude response of carriers with high mobility. The electrical control is achieved by gating the carrier density in a static magnetic field, opening new perspectives for applications like high-speed amplitude and phase modulators in the THz frequency range.

@article{shuvaev2013temperature, abstract = {We demonstrate electrical control of the room temperature Faraday effect in a 100-nm-thick film of strained HgTe, which is a topological insulator. The terahertz (THz) response of our device is dominated by the Drude response of carriers with high mobility. The electrical control is achieved by gating the carrier density in a static magnetic field, opening new perspectives for applications like high-speed amplitude and phase modulators in the THz frequency range.}, author = {Shuvaev, A and Pimenov, A and Astakhov, G. V. and Mühlbauer, M and Brüne, C and Buhmann, H and Molenkamp, L. W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {06}, number = 24, pages = {241902–}, publisher = {American Institute of Physics}, title = {Room temperature electrically tunable terahertz Faraday effect}, volume = 102, year = 2013 }

%0 Journal Article %1 shuvaev2013temperature %A Shuvaev, A %A Pimenov, A %A Astakhov, G. V. %A Mühlbauer, M %A Brüne, C %A Buhmann, H %A Molenkamp, L. W. %B Applied Physics Letters %D 2013 %I American Institute of Physics %J Appl. Phys. Lett. %N 24 %P 241902-- %R 10.1063/1.4811496 %T Room temperature electrically tunable terahertz Faraday effect %V 102 %X We demonstrate electrical control of the room temperature Faraday effect in a 100-nm-thick film of strained HgTe, which is a topological insulator. The terahertz (THz) response of our device is dominated by the Drude response of carriers with high mobility. The electrical control is achieved by gating the carrier density in a static magnetic field, opening new perspectives for applications like high-speed amplitude and phase modulators in the THz frequency range.
Imaging currents in {HgTe} quantum wells in the quantum spin Hall regime. Nowack, Katja C.; Spanton, Eric M.; Baenninger, Matthias; König, Markus; Kirtley, John R.; Kalisky, Beena; Ames, C.; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Goldhaber-Gordon, David; Moler, Kathryn A. In Nature Materials, 12(9), pp. 787–791. Springer Nature, 2013.
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The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.

@article{nowack2013imaging, abstract = {The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.}, author = {Nowack, Katja C. and Spanton, Eric M. and Baenninger, Matthias and König, Markus and Kirtley, John R. and Kalisky, Beena and Ames, C. and Leubner, Philipp and Brüne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Goldhaber-Gordon, David and Moler, Kathryn A.}, journal = {Nature Materials}, keywords = {qt}, month = {06}, number = 9, pages = {787–791}, publisher = {Springer Nature}, title = {Imaging currents in {HgTe} quantum wells in the quantum spin Hall regime}, volume = 12, year = 2013 }

%0 Journal Article %1 nowack2013imaging %A Nowack, Katja C. %A Spanton, Eric M. %A Baenninger, Matthias %A König, Markus %A Kirtley, John R. %A Kalisky, Beena %A Ames, C. %A Leubner, Philipp %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Goldhaber-Gordon, David %A Moler, Kathryn A. %D 2013 %I Springer Nature %J Nature Materials %N 9 %P 787--791 %R 10.1038/nmat3682 %T Imaging currents in {HgTe} quantum wells in the quantum spin Hall regime %V 12 %X The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.
Josephson Supercurrent through the Topological Surface States of Strained Bulk HgTe. Oostinga, Jeroen B.; Maier, Luis; Schüffelgen, Peter; Knott, Daniel; Ames, Christopher; Brüne, Christoph; Tkachov, Grigory; Buhmann, Hartmut; Molenkamp, Laurens W. In Phys. Rev. X, 3(2), p. 021007. American Physical Society, 2013.
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Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (∼30 000 cm^2/Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant 2π-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.

@article{oostinga2013josephson, abstract = {Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (∼30 000 cm^2/Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant 2π-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.}, author = {Oostinga, Jeroen B. and Maier, Luis and Sch\"uffelgen, Peter and Knott, Daniel and Ames, Christopher and Br\"une, Christoph and Tkachov, Grigory and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Phys. Rev. X}, keywords = {qt}, month = {05}, number = 2, pages = {021007}, publisher = {American Physical Society}, title = {Josephson Supercurrent through the Topological Surface States of Strained Bulk HgTe}, volume = 3, year = 2013 }

%0 Journal Article %1 oostinga2013josephson %A Oostinga, Jeroen B. %A Maier, Luis %A Schüffelgen, Peter %A Knott, Daniel %A Ames, Christopher %A Brüne, Christoph %A Tkachov, Grigory %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2013 %I American Physical Society %J Phys. Rev. X %N 2 %P 021007 %R 10.1103/PhysRevX.3.021007 %T Josephson Supercurrent through the Topological Surface States of Strained Bulk HgTe %V 3 %X Strained bulk HgTe is a three-dimensional topological insulator, whose surface electrons have a high mobility (∼30 000 cm^2/Vs), while its bulk is effectively free of mobile charge carriers. These properties enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant 2π-periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.
Spatially Resolved Study of Backscattering in the Quantum Spin Hall State. König, Markus; Baenninger, Matthias; Garcia, Andrei G. F.; Harjee, Nahid; Pruitt, Beth L.; Ames, C.; Leubner, Philipp; Brüne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Goldhaber-Gordon, David. In Phys. Rev. X, 3(2), p. 021003. American Physical Society, 2013.
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The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.

@article{PhysRevX.3.021003, abstract = {The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.}, author = {K\"onig, Markus and Baenninger, Matthias and Garcia, Andrei G. F. and Harjee, Nahid and Pruitt, Beth L. and Ames, C. and Leubner, Philipp and Br\"une, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Goldhaber-Gordon, David}, journal = {Phys. Rev. X}, keywords = {qt}, month = {04}, number = 2, pages = {021003}, publisher = {American Physical Society}, title = {Spatially Resolved Study of Backscattering in the Quantum Spin Hall State}, volume = 3, year = 2013 }

%0 Journal Article %1 PhysRevX.3.021003 %A König, Markus %A Baenninger, Matthias %A Garcia, Andrei G. F. %A Harjee, Nahid %A Pruitt, Beth L. %A Ames, C. %A Leubner, Philipp %A Brüne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Goldhaber-Gordon, David %D 2013 %I American Physical Society %J Phys. Rev. X %N 2 %P 021003 %R 10.1103/PhysRevX.3.021003 %T Spatially Resolved Study of Backscattering in the Quantum Spin Hall State %V 3 %X The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.
Terahertz quantum Hall effect of Dirac fermions in a topological insulator. Shuvaev, A. M.; Astakhov, G. V.; Tkachov, G.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; Pimenov, A. In Phys. Rev. B, 87(12), p. 121104. American Physical Society, 2013.
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Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.

@article{shuvaev2013terahertz, abstract = {Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.}, author = {Shuvaev, A. M. and Astakhov, G. V. and Tkachov, G. and Br\"une, C. and Buhmann, H. and Molenkamp, L. W. and Pimenov, A.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {03}, number = 12, pages = 121104, publisher = {American Physical Society}, title = {Terahertz quantum Hall effect of Dirac fermions in a topological insulator}, volume = 87, year = 2013 }

%0 Journal Article %1 shuvaev2013terahertz %A Shuvaev, A. M. %A Astakhov, G. V. %A Tkachov, G. %A Brüne, C. %A Buhmann, H. %A Molenkamp, L. W. %A Pimenov, A. %D 2013 %I American Physical Society %J Phys. Rev. B %N 12 %P 121104 %R 10.1103/PhysRevB.87.121104 %T Terahertz quantum Hall effect of Dirac fermions in a topological insulator %V 87 %X Using terahertz spectroscopy in external magnetic fields, we investigate the low-temperature charge dynamics of strained HgTe, a three-dimensional topological insulator. In resonator experiments, we observe quantum Hall oscillations at terahertz frequencies, which offer direct access to the unusual electrodynamic properties of the surface states of topological insulators. The 2D density estimated from the period of the quantum Hall oscillations agrees well with dc transport experiments on the topological surface state. The Dirac character of the surface state is further evidenced by the observation of the characteristic Berry phase in the dependence of the Landau levels on magnetic field.
Molecular beam epitaxy of high structural quality Bi2Se3 on lattice matched InP(111) substrates. Schreyeck, S; Tarakina, N. V.; Karczewski, G; Schumacher, C; Borzenko, T; Brüne, C; Buhmann, H; Gould, C; Brunner, K; Molenkamp, L. W. In Appl. Phys. Lett., 102(4), p. 041914-. American Institute of Physics, 2013.
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Epitaxial layers of the topological insulator Bi2Se3 have been grown by molecular beam epitaxy on laterally lattice-matched InP(111)B substrates. High resolution X-ray diffraction shows a significant improvement of Bi2Se3 crystal quality compared to layers deposited on other substrates. The measured full width at half maximum of the rocking curve is Δω=13 arc sec, and the (ω−2θ) scans exhibit clear layer thickness fringes. Atomic force microscope images show triangular twin domains with sizes increasing with layer thickness. The structural quality of the domains is confirmed on the microscopic level by transmission electron microscopy.

@article{schreyeck2013molecular, abstract = {Epitaxial layers of the topological insulator Bi2Se3 have been grown by molecular beam epitaxy on laterally lattice-matched InP(111)B substrates. High resolution X-ray diffraction shows a significant improvement of Bi2Se3 crystal quality compared to layers deposited on other substrates. The measured full width at half maximum of the rocking curve is Δω=13 arc sec, and the (ω−2θ) scans exhibit clear layer thickness fringes. Atomic force microscope images show triangular twin domains with sizes increasing with layer thickness. The structural quality of the domains is confirmed on the microscopic level by transmission electron microscopy.}, author = {Schreyeck, S and Tarakina, N. V. and Karczewski, G and Schumacher, C and Borzenko, T and Brüne, C and Buhmann, H and Gould, C and Brunner, K and Molenkamp, L. W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {01}, number = 4, pages = {041914–}, publisher = {American Institute of Physics}, title = {Molecular beam epitaxy of high structural quality Bi2Se3 on lattice matched InP(111) substrates}, volume = 102, year = 2013 }

%0 Journal Article %1 schreyeck2013molecular %A Schreyeck, S %A Tarakina, N. V. %A Karczewski, G %A Schumacher, C %A Borzenko, T %A Brüne, C %A Buhmann, H %A Gould, C %A Brunner, K %A Molenkamp, L. W. %B Applied Physics Letters %D 2013 %I American Institute of Physics %J Appl. Phys. Lett. %N 4 %P 041914-- %R 10.1063/1.4789775 %T Molecular beam epitaxy of high structural quality Bi2Se3 on lattice matched InP(111) substrates %V 102 %X Epitaxial layers of the topological insulator Bi2Se3 have been grown by molecular beam epitaxy on laterally lattice-matched InP(111)B substrates. High resolution X-ray diffraction shows a significant improvement of Bi2Se3 crystal quality compared to layers deposited on other substrates. The measured full width at half maximum of the rocking curve is Δω=13 arc sec, and the (ω−2θ) scans exhibit clear layer thickness fringes. Atomic force microscope images show triangular twin domains with sizes increasing with layer thickness. The structural quality of the domains is confirmed on the microscopic level by transmission electron microscopy.

Induced Superconductivity in the Three-Dimensional Topological Insulator HgTe. Maier, Luis; Oostinga, Jeroen B.; Knott, Daniel; Brüne, Christoph; Virtanen, Pauli; Tkachov, Grigory; Hankiewicz, Ewelina M.; Gould, Charles; Buhmann, Hartmut; Molenkamp, Laurens W. In Phys. Rev. Lett., 109(18), p. 186806. American Physical Society, 2012.
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A strained and undoped HgTe layer is a three-dimensional topological insulator, in which electronic transport occurs dominantly through its surface states. In this Letter, we present transport measurements on HgTe-based Josephson junctions with Nb as a superconductor. Although the Nb-HgTe interfaces have a low transparency, we observe a strong zero-bias anomaly in the differential resistance measurements. This anomaly originates from proximity-induced superconductivity in the HgTe surface states. In the most transparent junction, we observe periodic oscillations of the differential resistance as a function of an applied magnetic field, which correspond to a Fraunhofer-like pattern. This unambiguously shows that a precursor of the Josephson effect occurs in the topological surface states of HgTe.

@article{maier2012induced, abstract = {A strained and undoped HgTe layer is a three-dimensional topological insulator, in which electronic transport occurs dominantly through its surface states. In this Letter, we present transport measurements on HgTe-based Josephson junctions with Nb as a superconductor. Although the Nb-HgTe interfaces have a low transparency, we observe a strong zero-bias anomaly in the differential resistance measurements. This anomaly originates from proximity-induced superconductivity in the HgTe surface states. In the most transparent junction, we observe periodic oscillations of the differential resistance as a function of an applied magnetic field, which correspond to a Fraunhofer-like pattern. This unambiguously shows that a precursor of the Josephson effect occurs in the topological surface states of HgTe.}, author = {Maier, Luis and Oostinga, Jeroen B. and Knott, Daniel and Br\"une, Christoph and Virtanen, Pauli and Tkachov, Grigory and Hankiewicz, Ewelina M. and Gould, Charles and Buhmann, Hartmut and Molenkamp, Laurens W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = 11, number = 18, pages = 186806, publisher = {American Physical Society}, title = {Induced Superconductivity in the Three-Dimensional Topological Insulator HgTe}, volume = 109, year = 2012 }

%0 Journal Article %1 maier2012induced %A Maier, Luis %A Oostinga, Jeroen B. %A Knott, Daniel %A Brüne, Christoph %A Virtanen, Pauli %A Tkachov, Grigory %A Hankiewicz, Ewelina M. %A Gould, Charles %A Buhmann, Hartmut %A Molenkamp, Laurens W. %D 2012 %I American Physical Society %J Phys. Rev. Lett. %N 18 %P 186806 %R 10.1103/PhysRevLett.109.186806 %T Induced Superconductivity in the Three-Dimensional Topological Insulator HgTe %V 109 %X A strained and undoped HgTe layer is a three-dimensional topological insulator, in which electronic transport occurs dominantly through its surface states. In this Letter, we present transport measurements on HgTe-based Josephson junctions with Nb as a superconductor. Although the Nb-HgTe interfaces have a low transparency, we observe a strong zero-bias anomaly in the differential resistance measurements. This anomaly originates from proximity-induced superconductivity in the HgTe surface states. In the most transparent junction, we observe periodic oscillations of the differential resistance as a function of an applied magnetic field, which correspond to a Fraunhofer-like pattern. This unambiguously shows that a precursor of the Josephson effect occurs in the topological surface states of HgTe.
Fabrication of samples for scanning probe experiments on quantum spin Hall effect in HgTe quantum wells. Baenninger, M; König, M; Garcia, A. G. F.; Mühlbauer, M; Ames, C; Leubner, P; Brüne, C; Buhmann, H; Molenkamp, L. W.; Goldhaber-Gordon, D. In Journal of Applied Physics, 112(10), p. 103713-. American Institute of Physics, 2012.
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We present a fabrication process for devices on HgTe quantum wells through which the quantum spin Hall regime can be reached without the use of a top-gate electrode. We demonstrate that a nominally undoped HgTe quantum well can be tuned from p-type to n-type, crossing through the quantum spin Hall regime, using only a back-gate hundreds of microns away. Such structures will enable scanning probe investigations of the quantum spin Hall effect that would not be possible in the presence of a gate electrode on the surface of the wafer. All processes are kept below 80 °C to avoid degradation of the heat-sensitive HgTe quantum wells.

@article{baenninger2012fabrication, abstract = {We present a fabrication process for devices on HgTe quantum wells through which the quantum spin Hall regime can be reached without the use of a top-gate electrode. We demonstrate that a nominally undoped HgTe quantum well can be tuned from p-type to n-type, crossing through the quantum spin Hall regime, using only a back-gate hundreds of microns away. Such structures will enable scanning probe investigations of the quantum spin Hall effect that would not be possible in the presence of a gate electrode on the surface of the wafer. All processes are kept below 80 °C to avoid degradation of the heat-sensitive HgTe quantum wells.}, author = {Baenninger, M and König, M and Garcia, A. G. F. and Mühlbauer, M and Ames, C and Leubner, P and Brüne, C and Buhmann, H and Molenkamp, L. W. and Goldhaber-Gordon, D}, booktitle = {Journal of Applied Physics}, journal = {Journal of Applied Physics}, keywords = {qt}, month = 11, number = 10, pages = {103713–}, publisher = {American Institute of Physics}, title = {Fabrication of samples for scanning probe experiments on quantum spin Hall effect in HgTe quantum wells}, volume = 112, year = 2012 }

%0 Journal Article %1 baenninger2012fabrication %A Baenninger, M %A König, M %A Garcia, A. G. F. %A Mühlbauer, M %A Ames, C %A Leubner, P %A Brüne, C %A Buhmann, H %A Molenkamp, L. W. %A Goldhaber-Gordon, D %B Journal of Applied Physics %D 2012 %I American Institute of Physics %J Journal of Applied Physics %N 10 %P 103713-- %R 10.1063/1.4767362 %T Fabrication of samples for scanning probe experiments on quantum spin Hall effect in HgTe quantum wells %V 112 %X We present a fabrication process for devices on HgTe quantum wells through which the quantum spin Hall regime can be reached without the use of a top-gate electrode. We demonstrate that a nominally undoped HgTe quantum well can be tuned from p-type to n-type, crossing through the quantum spin Hall regime, using only a back-gate hundreds of microns away. Such structures will enable scanning probe investigations of the quantum spin Hall effect that would not be possible in the presence of a gate electrode on the surface of the wafer. All processes are kept below 80 °C to avoid degradation of the heat-sensitive HgTe quantum wells.
Spin polarization of the quantum spin Hall edge states. Brüne, Christoph; Roth, Andreas; Buhmann, Hartmut; Hankiewicz, Ewelina M.; Molenkamp, Laurens W.; Maciejko, Joseph; Qi, Xiao-Liang; Zhang, Shou-Cheng. In Nature Physics, 8(6), pp. 485–490. Springer Science and Business Media {LLC}, 2012.
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The prediction and experimental verification of the quantum spin Hall state marked the discovery of a new state of matter now known as topological insulators. Two-dimensional topological insulators exhibit the quantum spin-Hall effect, characterized by gapless spin-polarized counter-propagating edge channels. Whereas the helical character of these edge channels is now well established, experimental confirmation that the transport in the edge channels is spin polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin current injector and detector for the metallic spin Hall effect, and vice versa, allowing for an all-electrical detection of spin polarization.

@article{brne2012polarization, abstract = {The prediction and experimental verification of the quantum spin Hall state marked the discovery of a new state of matter now known as topological insulators. Two-dimensional topological insulators exhibit the quantum spin-Hall effect, characterized by gapless spin-polarized counter-propagating edge channels. Whereas the helical character of these edge channels is now well established, experimental confirmation that the transport in the edge channels is spin polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin current injector and detector for the metallic spin Hall effect, and vice versa, allowing for an all-electrical detection of spin polarization.}, author = {Brüne, Christoph and Roth, Andreas and Buhmann, Hartmut and Hankiewicz, Ewelina M. and Molenkamp, Laurens W. and Maciejko, Joseph and Qi, Xiao-Liang and Zhang, Shou-Cheng}, journal = {Nature Physics}, keywords = {qt}, month = {05}, number = 6, pages = {485–490}, publisher = {Springer Science and Business Media {LLC}}, title = {Spin polarization of the quantum spin Hall edge states}, volume = 8, year = 2012 }

%0 Journal Article %1 brne2012polarization %A Brüne, Christoph %A Roth, Andreas %A Buhmann, Hartmut %A Hankiewicz, Ewelina M. %A Molenkamp, Laurens W. %A Maciejko, Joseph %A Qi, Xiao-Liang %A Zhang, Shou-Cheng %D 2012 %I Springer Science and Business Media {LLC} %J Nature Physics %N 6 %P 485--490 %R 10.1038/nphys2322 %T Spin polarization of the quantum spin Hall edge states %V 8 %X The prediction and experimental verification of the quantum spin Hall state marked the discovery of a new state of matter now known as topological insulators. Two-dimensional topological insulators exhibit the quantum spin-Hall effect, characterized by gapless spin-polarized counter-propagating edge channels. Whereas the helical character of these edge channels is now well established, experimental confirmation that the transport in the edge channels is spin polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin current injector and detector for the metallic spin Hall effect, and vice versa, allowing for an all-electrical detection of spin polarization.
Comparative Study of the Microstructure of Bi2Se3 Thin Films Grown on Si(111) and {InP}(111) Substrates. Tarakina, N. V.; Schreyeck, S.; Borzenko, T.; Schumacher, C.; Karczewski, G.; Brunner, K.; Gould, C.; Buhmann, H.; Molenkamp, L. W. In Crystal Growth {\&} Design, 12(4), pp. 1913–1918. American Chemical Society ({ACS}), 2012.
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Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) have been carried out to clarify the microstructure of Bi2Se3 thin films grown by molecular beam epitaxy (MBE) on Si(111) and InP(111) substrates. The film grown on InP displays much better overall quality at the microstructural level than does the film grown on the Si substrate. A layer of poor crystalline quality at the interface followed by well-crystallized Bi2Se3 has been observed for both substrates. The thickness of this interface layer is not uniform; it varies across the sample from zero, showing a sharp interface between the substrate and Bi2Se3, up to ∼1 nm and ∼1.8 nm for Bi2Se3/InP and Bi2Se3/Si, respectively. Formation of rotation twin domains and lamellar twins has been observed and is described in detail for both substrates.

@article{tarakina2012comparative, abstract = {Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) have been carried out to clarify the microstructure of Bi2Se3 thin films grown by molecular beam epitaxy (MBE) on Si(111) and InP(111) substrates. The film grown on InP displays much better overall quality at the microstructural level than does the film grown on the Si substrate. A layer of poor crystalline quality at the interface followed by well-crystallized Bi2Se3 has been observed for both substrates. The thickness of this interface layer is not uniform; it varies across the sample from zero, showing a sharp interface between the substrate and Bi2Se3, up to ∼1 nm and ∼1.8 nm for Bi2Se3/InP and Bi2Se3/Si, respectively. Formation of rotation twin domains and lamellar twins has been observed and is described in detail for both substrates.}, author = {Tarakina, N. V. and Schreyeck, S. and Borzenko, T. and Schumacher, C. and Karczewski, G. and Brunner, K. and Gould, C. and Buhmann, H. and Molenkamp, L. W.}, journal = {Crystal Growth {\&} Design}, keywords = {qt}, month = {03}, number = 4, pages = {1913–1918}, publisher = {American Chemical Society ({ACS})}, title = {Comparative Study of the Microstructure of Bi2Se3 Thin Films Grown on Si(111) and {InP}(111) Substrates}, volume = 12, year = 2012 }

%0 Journal Article %1 tarakina2012comparative %A Tarakina, N. V. %A Schreyeck, S. %A Borzenko, T. %A Schumacher, C. %A Karczewski, G. %A Brunner, K. %A Gould, C. %A Buhmann, H. %A Molenkamp, L. W. %D 2012 %I American Chemical Society ({ACS}) %J Crystal Growth {\&} Design %N 4 %P 1913--1918 %R 10.1021/cg201636g %T Comparative Study of the Microstructure of Bi2Se3 Thin Films Grown on Si(111) and {InP}(111) Substrates %V 12 %X Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) have been carried out to clarify the microstructure of Bi2Se3 thin films grown by molecular beam epitaxy (MBE) on Si(111) and InP(111) substrates. The film grown on InP displays much better overall quality at the microstructural level than does the film grown on the Si substrate. A layer of poor crystalline quality at the interface followed by well-crystallized Bi2Se3 has been observed for both substrates. The thickness of this interface layer is not uniform; it varies across the sample from zero, showing a sharp interface between the substrate and Bi2Se3, up to ∼1 nm and ∼1.8 nm for Bi2Se3/InP and Bi2Se3/Si, respectively. Formation of rotation twin domains and lamellar twins has been observed and is described in detail for both substrates.
Terahertz magneto-optical spectroscopy in HgTe thin films. Shuvaev, A M; Astakhov, G V; Brüne, C; Buhmann, H; Molenkamp, L W; Pimenov, A. In Semiconductor Science and Technology, 27, p. 124004. 2012.
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Thin films of HgTe have been systematically investigated using continuous frequency terahertz spectroscopy in external magnetic fields. In these experiments, full control of the polarization state can be achieved including Faraday rotation and ellipticity. We present the details of the experimental procedure and of the data analysis. Besides the cyclotron resonance, an additional mode is observed in the zero-gap sample. The results at high temperatures can be well understood within the classical Drude model of the dynamic conductivity. Possible dimensionality of the charge dynamics at low temperatures is discussed.

@article{shuvaev2012terahertz, abstract = {Thin films of HgTe have been systematically investigated using continuous frequency terahertz spectroscopy in external magnetic fields. In these experiments, full control of the polarization state can be achieved including Faraday rotation and ellipticity. We present the details of the experimental procedure and of the data analysis. Besides the cyclotron resonance, an additional mode is observed in the zero-gap sample. The results at high temperatures can be well understood within the classical Drude model of the dynamic conductivity. Possible dimensionality of the charge dynamics at low temperatures is discussed.}, author = {Shuvaev, A M and Astakhov, G V and Brüne, C and Buhmann, H and Molenkamp, L W and Pimenov, A}, journal = {Semiconductor Science and Technology}, keywords = {qt}, month = {02}, pages = 124004, title = {Terahertz magneto-optical spectroscopy in HgTe thin films}, volume = 27, year = 2012 }

%0 Journal Article %1 shuvaev2012terahertz %A Shuvaev, A M %A Astakhov, G V %A Brüne, C %A Buhmann, H %A Molenkamp, L W %A Pimenov, A %D 2012 %J Semiconductor Science and Technology %P 124004 %R 10.1088/0268-1242/27/12/124004 %T Terahertz magneto-optical spectroscopy in HgTe thin films %V 27 %X Thin films of HgTe have been systematically investigated using continuous frequency terahertz spectroscopy in external magnetic fields. In these experiments, full control of the polarization state can be achieved including Faraday rotation and ellipticity. We present the details of the experimental procedure and of the data analysis. Besides the cyclotron resonance, an additional mode is observed in the zero-gap sample. The results at high temperatures can be well understood within the classical Drude model of the dynamic conductivity. Possible dimensionality of the charge dynamics at low temperatures is discussed.

The quantum spin Hall effect. Buhmann, Hartmut. In Journal of Applied Physics, 109(10), bl 102409-. American Institute of Physics, 2011.
The detection of terahertz waves by semimetallic and by semiconducting materials. Gouider, F; Nachtwei, G; Brüne, C; Buhmann, H; Vasilyev, Yu. B.; Salman, M; Könemann, J; Buckle, P. D. In Journal of Applied Physics, 109(1), bl 013106-. American Institute of Physics, 2011.
Surface State Charge Dynamics of a High-Mobility Three-Dimensional Topological Insulator. Hancock, Jason N.; van Mechelen, J. L. M.; Kuzmenko, Alexey B.; van der Marel, Dirk; Brüne, Christoph; Novik, Elena G.; Astakhov, Georgy V.; Buhmann, Hartmut; Molenkamp, Laurens W. In Phys. Rev. Lett., 107(13), bl 136803. American Physical Society, 2011.
Single valley Dirac fermions in zero-gap {HgTe} quantum wells. Büttner, B.; Liu, C. X.; Tkachov, G.; Novik, E. G.; Brüne, C.; Buhmann, H.; Hankiewicz, E. M.; Recher, P.; Trauzettel, B.; Zhang, S. C.; Molenkamp, L. W. In Nature Physics, 7(5), bll 418–422. Springer Science and Business Media {LLC}, 2011.
Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe. Brüne, C.; Liu, C. X.; Novik, E. G.; Hankiewicz, E. M.; Buhmann, H.; Chen, Y. L.; Qi, X. L.; Shen, Z. X.; Zhang, S. C.; Molenkamp, L. W. In Phys. Rev. Lett., 106(12), bl 126803. American Physical Society, 2011.
Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range. Shuvaev, A. M.; Astakhov, G. V.; Pimenov, A.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Lett., 106(10), bl 107404. American Physical Society, 2011.
Fine structure of zero-mode Landau levels in HgTe/Hg${}_{x}$Cd${}_{1\ensuremath{-}x}$Te quantum wells. Orlita, M.; Masztalerz, K.; Faugeras, C.; Potemski, M.; Novik, E. G.; Brüne, C.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 83(11), bl 115307. American Physical Society, 2011.
Backscattering of Dirac Fermions in HgTe Quantum Wells with a Finite Gap. Tkachov, G.; Thienel, C.; Pinneker, V.; Büttner, B.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; Hankiewicz, E. M. In Phys. Rev. Lett., 106(7), bl 076802. American Physical Society, 2011.

Terahertz photoconductivity of a two-dimensional electron gas in {HgCdTe}/{HgTe} quantum wells. Vasilyev, Yu. B.; Gouider, F.; Bug{{á}}r, M.; Nachtwei, G.; Könemann, J.; Brüne, C.; Buhmann, H. In physica status solidi (b), 247(6), pp. 1495–1497. Wiley, 2010.
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The terahertz (THz) photoconductivity is investigated in HgTe/HgCdTe‐quantum wells (QWs) in Corbino geometry at various wavelengths of excited radiation. The radiation source is a p‐Ge cyclotron laser (pulse width about 1 µs, repetition rate 1 Hz) which is tunable in the wavelength range 120 µm < λ < 180 µm by an external magnetic field. It is shown that the photoconductivity is caused by the heating of two‐dimensional electron gas (2DEG). A rough estimation yields relaxation time around 0.46 µs. Because of the low effective mass, this material system is especially interesting for detector applications.

@article{vasilyev2010terahertz, abstract = {The terahertz (THz) photoconductivity is investigated in HgTe/HgCdTe‐quantum wells (QWs) in Corbino geometry at various wavelengths of excited radiation. The radiation source is a p‐Ge cyclotron laser (pulse width about 1 µs, repetition rate 1 Hz) which is tunable in the wavelength range 120 µm < λ < 180 µm by an external magnetic field. It is shown that the photoconductivity is caused by the heating of two‐dimensional electron gas (2DEG). A rough estimation yields relaxation time around 0.46 µs. Because of the low effective mass, this material system is especially interesting for detector applications.}, author = {Vasilyev, Yu. B. and Gouider, F. and Bug{\'{a}}r, M. and Nachtwei, G. and Könemann, J. and Brüne, C. and Buhmann, H.}, journal = {physica status solidi (b)}, keywords = {qt}, month = {03}, number = 6, pages = {1495–1497}, publisher = {Wiley}, title = {Terahertz photoconductivity of a two-dimensional electron gas in {HgCdTe}/{HgTe} quantum wells}, volume = 247, year = 2010 }

%0 Journal Article %1 vasilyev2010terahertz %A Vasilyev, Yu. B. %A Gouider, F. %A Bug{{á}}r, M. %A Nachtwei, G. %A Könemann, J. %A Brüne, C. %A Buhmann, H. %D 2010 %I Wiley %J physica status solidi (b) %N 6 %P 1495--1497 %R 10.1002/pssb.200983180 %T Terahertz photoconductivity of a two-dimensional electron gas in {HgCdTe}/{HgTe} quantum wells %V 247 %X The terahertz (THz) photoconductivity is investigated in HgTe/HgCdTe‐quantum wells (QWs) in Corbino geometry at various wavelengths of excited radiation. The radiation source is a p‐Ge cyclotron laser (pulse width about 1 µs, repetition rate 1 Hz) which is tunable in the wavelength range 120 µm < λ < 180 µm by an external magnetic field. It is shown that the photoconductivity is caused by the heating of two‐dimensional electron gas (2DEG). A rough estimation yields relaxation time around 0.46 µs. Because of the low effective mass, this material system is especially interesting for detector applications.
Quantum tunneling through planar p–n junctions in HgTe quantum wells. Zhang, L B; Chang, K; Xie, X C; Buhmann, H; Molenkamp, L W. In New Journal of Physics, 12, p. 083058. 2010.
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We demonstrate that a p–n junction created electrically in HgTe quantum wells with inverted band structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p–n junction. The opacity and transparency of electrons through the p–n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin–orbit interaction (RSOI). The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional (Q1D) p–n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong RSOI.

@article{zhang2010quantum, abstract = {We demonstrate that a p–n junction created electrically in HgTe quantum wells with inverted band structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p–n junction. The opacity and transparency of electrons through the p–n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin–orbit interaction (RSOI). The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional (Q1D) p–n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong RSOI.}, author = {Zhang, L B and Chang, K and Xie, X C and Buhmann, H and Molenkamp, L W}, journal = {New Journal of Physics}, keywords = {qt}, month = 10, pages = {083058}, title = {Quantum tunneling through planar p–n junctions in HgTe quantum wells}, volume = 12, year = 2010 }

%0 Journal Article %1 zhang2010quantum %A Zhang, L B %A Chang, K %A Xie, X C %A Buhmann, H %A Molenkamp, L W %D 2010 %J New Journal of Physics %P 083058 %R 10.1088/1367-2630/12/8/083058 %T Quantum tunneling through planar p–n junctions in HgTe quantum wells %V 12 %X We demonstrate that a p–n junction created electrically in HgTe quantum wells with inverted band structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p–n junction. The opacity and transparency of electrons through the p–n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin–orbit interaction (RSOI). The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional (Q1D) p–n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong RSOI.
Magnetotransport and THz-Optical Investigations at Devices with HgTe Quantum Wells. Gouider, F.; Vasilyev, Y. B.; Bug{á}r, M.; K{ö}nemann, J.; Br{ü}ne, C.; Buhmann, H.; Nachtwei, G. In Journal of Low Temperature Physics, 159(1), pp. 184–188. 2010.
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We investigated the magnetoconductivity and the Terahertz (THz) photo-conductivity of devices with HgTe quantum wells embedded in barrier layers of HgCdTe. For the photoconductivity measurements, a THz laser system (p-Ge-Laser) is applied. This laser uses transitions between Landau levels of light holes in Ge and emits laser pulses in the wavelength range 120 $\mu$m < $\lambda$ < 180 $\mu$m. The THz laser radiation is used in order to excite charge carriers over the Landau-gap. The response of the sample to the laser impulses is in 2D-samples in the quantum Hall (QH) regime measured in order to receive data of the relaxation of the charge carriers. In this presentation we present photoconduction measurements of the HgTe-quantum well in Hall bar, Corbino as well as combined Corbino-Hall bar geometry in the QH-regime. The material system HgTe/HgCdTe is characterized by a small effective mass (compared to GaAs, in our case 0.023 m0) and accordingly smaller magnetic fields for the appropriate cyclotron energy. Thus, this material combination provides the opportunity to make THz detectors using magnetic fields below 2 T for operation.

@article{gouider2010magnetotransport, abstract = {We investigated the magnetoconductivity and the Terahertz (THz) photo-conductivity of devices with HgTe quantum wells embedded in barrier layers of HgCdTe. For the photoconductivity measurements, a THz laser system (p-Ge-Laser) is applied. This laser uses transitions between Landau levels of light holes in Ge and emits laser pulses in the wavelength range 120 $\mu$m < $\lambda$ < 180 $\mu$m. The THz laser radiation is used in order to excite charge carriers over the Landau-gap. The response of the sample to the laser impulses is in 2D-samples in the quantum Hall (QH) regime measured in order to receive data of the relaxation of the charge carriers. In this presentation we present photoconduction measurements of the HgTe-quantum well in Hall bar, Corbino as well as combined Corbino-Hall bar geometry in the QH-regime. The material system HgTe/HgCdTe is characterized by a small effective mass (compared to GaAs, in our case 0.023 m0) and accordingly smaller magnetic fields for the appropriate cyclotron energy. Thus, this material combination provides the opportunity to make THz detectors using magnetic fields below 2 T for operation.}, author = {Gouider, F. and Vasilyev, Y. B. and Bug{\'a}r, M. and K{\"o}nemann, J. and Br{\"u}ne, C. and Buhmann, H. and Nachtwei, G.}, journal = {Journal of Low Temperature Physics}, keywords = {qt}, month = {04}, number = 1, pages = {184–188}, title = {Magnetotransport and THz-Optical Investigations at Devices with HgTe Quantum Wells}, volume = 159, year = 2010 }

%0 Journal Article %1 gouider2010magnetotransport %A Gouider, F. %A Vasilyev, Y. B. %A Bug{á}r, M. %A K{ö}nemann, J. %A Br{ü}ne, C. %A Buhmann, H. %A Nachtwei, G. %D 2010 %J Journal of Low Temperature Physics %N 1 %P 184--188 %R 10.1007/s10909-009-0115-5 %T Magnetotransport and THz-Optical Investigations at Devices with HgTe Quantum Wells %V 159 %X We investigated the magnetoconductivity and the Terahertz (THz) photo-conductivity of devices with HgTe quantum wells embedded in barrier layers of HgCdTe. For the photoconductivity measurements, a THz laser system (p-Ge-Laser) is applied. This laser uses transitions between Landau levels of light holes in Ge and emits laser pulses in the wavelength range 120 $\mu$m < $\lambda$ < 180 $\mu$m. The THz laser radiation is used in order to excite charge carriers over the Landau-gap. The response of the sample to the laser impulses is in 2D-samples in the quantum Hall (QH) regime measured in order to receive data of the relaxation of the charge carriers. In this presentation we present photoconduction measurements of the HgTe-quantum well in Hall bar, Corbino as well as combined Corbino-Hall bar geometry in the QH-regime. The material system HgTe/HgCdTe is characterized by a small effective mass (compared to GaAs, in our case 0.023 m0) and accordingly smaller magnetic fields for the appropriate cyclotron energy. Thus, this material combination provides the opportunity to make THz detectors using magnetic fields below 2 T for operation.
Evidence for the ballistic intrinsic spin Hall effect in {HgTe} nanostructures. Brüne, C.; Roth, A.; Novik, E. G.; König, M.; Buhmann, H.; Hankiewicz, E. M.; Hanke, W.; Sinova, J.; Molenkamp, L. W. In Nature Physics, 6(6), pp. 448–454. Springer Science and Business Media {LLC}, 2010.
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In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.

@article{brne2010evidence, abstract = {In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.}, author = {Brüne, C. and Roth, A. and Novik, E. G. and König, M. and Buhmann, H. and Hankiewicz, E. M. and Hanke, W. and Sinova, J. and Molenkamp, L. W.}, journal = {Nature Physics}, keywords = {qt}, month = {05}, number = 6, pages = {448–454}, publisher = {Springer Science and Business Media {LLC}}, title = {Evidence for the ballistic intrinsic spin Hall effect in {HgTe} nanostructures}, volume = 6, year = 2010 }

%0 Journal Article %1 brne2010evidence %A Brüne, C. %A Roth, A. %A Novik, E. G. %A König, M. %A Buhmann, H. %A Hankiewicz, E. M. %A Hanke, W. %A Sinova, J. %A Molenkamp, L. W. %D 2010 %I Springer Science and Business Media {LLC} %J Nature Physics %N 6 %P 448--454 %R 10.1038/nphys1655 %T Evidence for the ballistic intrinsic spin Hall effect in {HgTe} nanostructures %V 6 %X In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.
Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures. Brüne, C.; Roth, A.; Novik, E. G.; König, M.; Buhmann, H.; Hankiewicz, E. M.; Hanke, W.; Sinova, J.; Molenkamp, L. W. In Nature Physics, 6, pp. 448–454. Nature Publishing Group, 2010.
- [ Abstract ]
- [ BibTeX ]
- [ EndNote ]
- [ DOI ]
In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.

@article{brune2010evidence, abstract = {In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.}, author = {Brüne, C. and Roth, A. and Novik, E. G. and König, M. and Buhmann, H. and Hankiewicz, E. M. and Hanke, W. and Sinova, J. and Molenkamp, L. W.}, journal = {Nature Physics}, keywords = {qt}, month = {05}, pages = {448–454}, publisher = {Nature Publishing Group}, title = {Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures}, volume = 6, year = 2010 }

%0 Journal Article %1 brune2010evidence %A Brüne, C. %A Roth, A. %A Novik, E. G. %A König, M. %A Buhmann, H. %A Hankiewicz, E. M. %A Hanke, W. %A Sinova, J. %A Molenkamp, L. W. %D 2010 %I Nature Publishing Group %J Nature Physics %P 448--454 %R 10.1038/nphys1655 %T Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures %V 6 %X In the spin Hall effect, a current passed through a spin–orbit coupled electron gas induces a spin accumulation of inverse sign on either side of the sample. A number of possible mechanisms have been described, extrinsic as well as intrinsic ones, and they may occur in the ballistic as well as the diffusive transport regime. A central problem for experimentalists in studying the effect is the very small signals that result from the spin accumulation. Electrical measurements on metals have yielded reliable signatures of the spin Hall effect, but in semiconductors the spin accumulation could only be detected by optical techniques. Here we report experimental evidence for electrical manipulation and detection of the ballistic intrinsic spin Hall effect (ISHE) in semiconductors. We perform a non-local electrical measurement in nanoscale H-shaped structures built on high-mobility HgTe/(Hg, Cd)Te quantum wells. When the samples are tuned into the p-regime, we observe a large non-local resistance signal due to the ISHE, several orders of magnitude larger than in metals. In the n-regime, where the spin–orbit splitting is reduced, the signal is at least one order of magnitude smaller and vanishes for narrower quantum wells. We verify our experimental observations by quantum transport calculations.
Circular photogalvanic effect in HgTe/CdHgTe quantum well structures. Wittmann, B; Danilov, S N; Bel’kov, V V; Dvoretsky, S A; Vinh, N Q; van der Meer, A F G; Murdin, B; Ganichev, S D; Tarasenko, S A; Novik, E G; Buhmann, H; Brüne, C; Molenkamp, L W; Kvon, Z D; Mikhailov, N N. In Semiconductor Science and Technology, 25, p. 095005. 2010.
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We describe the observation of the circular and linear photogalvanic effects in HgTe/CdHgTe quantum wells. The interband absorption of mid-infrared radiation as well as the intrasubband absorption of terahertz radiation in the quantun well structures is shown to cause a dc electric current due to these effects. The photocurrent magnitude and direction varies with the radiation polarization state and crystallographic orientation of the substrate in a simple way that can be understood from a phenomenological theory. The observed dependences of the photocurrent on the radiation wavelength and temperature are discussed in terms of a microscopic model.

@article{wittmann2010circular, abstract = {We describe the observation of the circular and linear photogalvanic effects in HgTe/CdHgTe quantum wells. The interband absorption of mid-infrared radiation as well as the intrasubband absorption of terahertz radiation in the quantun well structures is shown to cause a dc electric current due to these effects. The photocurrent magnitude and direction varies with the radiation polarization state and crystallographic orientation of the substrate in a simple way that can be understood from a phenomenological theory. The observed dependences of the photocurrent on the radiation wavelength and temperature are discussed in terms of a microscopic model.}, author = {Wittmann, B and Danilov, S N and Bel'kov, V V and Dvoretsky, S A and Vinh, N Q and van der Meer, A F G and Murdin, B and Ganichev, S D and Tarasenko, S A and Novik, E G and Buhmann, H and Brüne, C and Molenkamp, L W and Kvon, Z D and Mikhailov, N N}, journal = {Semiconductor Science and Technology}, keywords = {qt}, month = 11, pages = {095005}, title = {Circular photogalvanic effect in HgTe/CdHgTe quantum well structures}, volume = 25, year = 2010 }

%0 Journal Article %1 wittmann2010circular %A Wittmann, B %A Danilov, S N %A Bel'kov, V V %A Dvoretsky, S A %A Vinh, N Q %A van der Meer, A F G %A Murdin, B %A Ganichev, S D %A Tarasenko, S A %A Novik, E G %A Buhmann, H %A Brüne, C %A Molenkamp, L W %A Kvon, Z D %A Mikhailov, N N %D 2010 %J Semiconductor Science and Technology %P 095005 %R 10.1088/0268-1242/25/9/095005 %T Circular photogalvanic effect in HgTe/CdHgTe quantum well structures %V 25 %X We describe the observation of the circular and linear photogalvanic effects in HgTe/CdHgTe quantum wells. The interband absorption of mid-infrared radiation as well as the intrasubband absorption of terahertz radiation in the quantun well structures is shown to cause a dc electric current due to these effects. The photocurrent magnitude and direction varies with the radiation polarization state and crystallographic orientation of the substrate in a simple way that can be understood from a phenomenological theory. The observed dependences of the photocurrent on the radiation wavelength and temperature are discussed in terms of a microscopic model.

Spin Hall Effects in HgTe Quantum Well Structures. Buhmann, Hartmut. In International Journal of Modern Physics B, 23(12n13), pp. 2551–2555. 2009.
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Due to a strong spin orbit interaction quantum well structures exhibit an unusual subband structure ordering which leads to some remarkable transport properties depending on the actual carrier density. Especially for quantum wells with an inverted band structure ordering, a strong Rashba-type spin orbit splitting gives rise to a strong spin Hall effect in the metallic regime and in the bulk insulating regime spin polarized edge channel transport leads to the formation of the quantum spin Hall effect. Gated quantum well structures have been used to explore these, the metallic and insulating, transport regimes experimentally.

@article{buhmann2009effects, abstract = {Due to a strong spin orbit interaction quantum well structures exhibit an unusual subband structure ordering which leads to some remarkable transport properties depending on the actual carrier density. Especially for quantum wells with an inverted band structure ordering, a strong Rashba-type spin orbit splitting gives rise to a strong spin Hall effect in the metallic regime and in the bulk insulating regime spin polarized edge channel transport leads to the formation of the quantum spin Hall effect. Gated quantum well structures have been used to explore these, the metallic and insulating, transport regimes experimentally.}, author = {Buhmann, Hartmut}, journal = {International Journal of Modern Physics B}, keywords = {qt}, month = {05}, number = {12n13}, pages = {2551–2555}, title = {Spin Hall Effects in HgTe Quantum Well Structures}, volume = 23, year = 2009 }

%0 Journal Article %1 buhmann2009effects %A Buhmann, Hartmut %D 2009 %J International Journal of Modern Physics B %N 12n13 %P 2551--2555 %R 10.1142/S0217979209061974 %T Spin Hall Effects in HgTe Quantum Well Structures %V 23 %X Due to a strong spin orbit interaction quantum well structures exhibit an unusual subband structure ordering which leads to some remarkable transport properties depending on the actual carrier density. Especially for quantum wells with an inverted band structure ordering, a strong Rashba-type spin orbit splitting gives rise to a strong spin Hall effect in the metallic regime and in the bulk insulating regime spin polarized edge channel transport leads to the formation of the quantum spin Hall effect. Gated quantum well structures have been used to explore these, the metallic and insulating, transport regimes experimentally.
Nonlocal Transport in the Quantum Spin Hall State. Roth, Andreas; Br{ü}ne, Christoph; Buhmann, Hartmut; Molenkamp, Laurens W.; Maciejko, Joseph; Qi, Xiao-Liang; Zhang, Shou-Cheng. In Science, 325(5938), pp. 294–297. American Association for the Advancement of Science, 2009.
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Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.

@article{roth2009nonlocal, abstract = {Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.}, author = {Roth, Andreas and Br{\"u}ne, Christoph and Buhmann, Hartmut and Molenkamp, Laurens W. and Maciejko, Joseph and Qi, Xiao-Liang and Zhang, Shou-Cheng}, journal = {Science}, keywords = {qt}, number = 5938, pages = {294–297}, publisher = {American Association for the Advancement of Science}, title = {Nonlocal Transport in the Quantum Spin Hall State}, volume = 325, year = 2009 }

%0 Journal Article %1 roth2009nonlocal %A Roth, Andreas %A Br{ü}ne, Christoph %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Maciejko, Joseph %A Qi, Xiao-Liang %A Zhang, Shou-Cheng %D 2009 %I American Association for the Advancement of Science %J Science %N 5938 %P 294--297 %R 10.1126/science.1174736 %T Nonlocal Transport in the Quantum Spin Hall State %V 325 %X Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.
Nonlinear magnetogyrotropic photogalvanic effect. Diehl, H.; Shalygin, V. A.; Golub, L. E.; Tarasenko, S. A.; Danilov, S. N.; Bel’kov, V. V.; Novik, E. G.; Buhmann, H.; Brüne, C.; Molenkamp, L. W.; Ivchenko, E. L.; Ganichev, S. D. In Phys. Rev. B, 80(7), p. 075311. American Physical Society, 2009.
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We report on the observation of magnetic-field-induced photocurrent in HgTe/HgCdTe quantum wells of different widths. Both the intrasubband and interband absorption of infrared/terahertz radiation in the heterostructures is shown to cause a dc electric current in the presence of an in-plane magnetic field. The photocurrent behavior upon variation in the radiation polarization, magnetic-field strength, and temperature is studied. At a moderate magnetic field the current exhibits a linear field dependence. At high magnetic fields, however, it becomes nonlinear and is dominated by a cubic in magnetic-field contribution. The latter effect is observed in quantum wells with the inverted band structure only. The experimental results are analyzed in terms of the phenomenological theory and microscopic models of magnetogyrotropic photogalvanic effect based on asymmetry of optical transitions and/or asymmetric relaxation of carriers in the momentum space. The effect is shown to be related to the gyrotropic properties of the structures. The developed theory of magnetogyrotropic photocurrent describes well all experimental results. It is shown that both intrasubband and interband optical transitions may lead to spin-related as well as to spin-independent magnetic-field-induced photocurrents.

@article{diehl2009nonlinear, abstract = {We report on the observation of magnetic-field-induced photocurrent in HgTe/HgCdTe quantum wells of different widths. Both the intrasubband and interband absorption of infrared/terahertz radiation in the heterostructures is shown to cause a dc electric current in the presence of an in-plane magnetic field. The photocurrent behavior upon variation in the radiation polarization, magnetic-field strength, and temperature is studied. At a moderate magnetic field the current exhibits a linear field dependence. At high magnetic fields, however, it becomes nonlinear and is dominated by a cubic in magnetic-field contribution. The latter effect is observed in quantum wells with the inverted band structure only. The experimental results are analyzed in terms of the phenomenological theory and microscopic models of magnetogyrotropic photogalvanic effect based on asymmetry of optical transitions and/or asymmetric relaxation of carriers in the momentum space. The effect is shown to be related to the gyrotropic properties of the structures. The developed theory of magnetogyrotropic photocurrent describes well all experimental results. It is shown that both intrasubband and interband optical transitions may lead to spin-related as well as to spin-independent magnetic-field-induced photocurrents.}, author = {Diehl, H. and Shalygin, V. A. and Golub, L. E. and Tarasenko, S. A. and Danilov, S. N. and Bel'kov, V. V. and Novik, E. G. and Buhmann, H. and Br\"une, C. and Molenkamp, L. W. and Ivchenko, E. L. and Ganichev, S. D.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {08}, number = 7, pages = {075311}, publisher = {American Physical Society}, title = {Nonlinear magnetogyrotropic photogalvanic effect}, volume = 80, year = 2009 }

%0 Journal Article %1 diehl2009nonlinear %A Diehl, H. %A Shalygin, V. A. %A Golub, L. E. %A Tarasenko, S. A. %A Danilov, S. N. %A Bel'kov, V. V. %A Novik, E. G. %A Buhmann, H. %A Brüne, C. %A Molenkamp, L. W. %A Ivchenko, E. L. %A Ganichev, S. D. %D 2009 %I American Physical Society %J Phys. Rev. B %N 7 %P 075311 %R 10.1103/PhysRevB.80.075311 %T Nonlinear magnetogyrotropic photogalvanic effect %V 80 %X We report on the observation of magnetic-field-induced photocurrent in HgTe/HgCdTe quantum wells of different widths. Both the intrasubband and interband absorption of infrared/terahertz radiation in the heterostructures is shown to cause a dc electric current in the presence of an in-plane magnetic field. The photocurrent behavior upon variation in the radiation polarization, magnetic-field strength, and temperature is studied. At a moderate magnetic field the current exhibits a linear field dependence. At high magnetic fields, however, it becomes nonlinear and is dominated by a cubic in magnetic-field contribution. The latter effect is observed in quantum wells with the inverted band structure only. The experimental results are analyzed in terms of the phenomenological theory and microscopic models of magnetogyrotropic photogalvanic effect based on asymmetry of optical transitions and/or asymmetric relaxation of carriers in the momentum space. The effect is shown to be related to the gyrotropic properties of the structures. The developed theory of magnetogyrotropic photocurrent describes well all experimental results. It is shown that both intrasubband and interband optical transitions may lead to spin-related as well as to spin-independent magnetic-field-induced photocurrents.

The Quantum Spin Hall Effect: Theory and Experiment. König, Markus; Buhmann, Hartmut; Molenkamp, Laurens W.; Hughes, Taylor; Liu, Chao-Xing; Qi, Xiao-Liang; Zhang, Shou-Cheng. In Journal of the Physical Society of Japan, 77(3), p. 031007. Physical Society of Japan, 2008.
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The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells (QWs). By varying the thickness of the QW, the band structure changes from a normal to an “inverted” type at a critical thickness d c . We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te QWs. We review both the fabrication of the sample and the experimental setup. For thin QWs with well width d QW <6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker QWs ( d QW >6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2 e^2 / h . The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d c =6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.

@article{knig2008quantum, abstract = {The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells (QWs). By varying the thickness of the QW, the band structure changes from a normal to an “inverted” type at a critical thickness d c . We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te QWs. We review both the fabrication of the sample and the experimental setup. For thin QWs with well width d QW <6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker QWs ( d QW >6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2 e^2 / h . The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d c =6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.}, author = {König, Markus and Buhmann, Hartmut and Molenkamp, Laurens W. and Hughes, Taylor and Liu, Chao-Xing and Qi, Xiao-Liang and Zhang, Shou-Cheng}, journal = {Journal of the Physical Society of Japan}, keywords = {qt}, month = {03}, number = 3, pages = {031007}, publisher = {Physical Society of Japan}, title = {The Quantum Spin Hall Effect: Theory and Experiment}, volume = 77, year = 2008 }

%0 Journal Article %1 knig2008quantum %A König, Markus %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Hughes, Taylor %A Liu, Chao-Xing %A Qi, Xiao-Liang %A Zhang, Shou-Cheng %D 2008 %I Physical Society of Japan %J Journal of the Physical Society of Japan %N 3 %P 031007 %R 10.1143/jpsj.77.031007 %T The Quantum Spin Hall Effect: Theory and Experiment %V 77 %X The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells (QWs). By varying the thickness of the QW, the band structure changes from a normal to an “inverted” type at a critical thickness d c . We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te QWs. We review both the fabrication of the sample and the experimental setup. For thin QWs with well width d QW <6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker QWs ( d QW >6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2 e^2 / h . The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d c =6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.
Quantum dot as thermal rectifier. Scheibner, R; König, M; Reuter, D; Wieck, A D; Gould, C; Buhmann, H; Molenkamp, L W. In New Journal of Physics, 10(8), p. 083016. 2008.
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We report the observation of thermal rectification in a semiconductor quantum dot, as inferred from the asymmetric line shape of the thermopower oscillations. The asymmetry is observed at high in-plane magnetic fields and caused by the presence of a high orbital momentum state in the dot.

@article{scheibner2008quantum, abstract = {We report the observation of thermal rectification in a semiconductor quantum dot, as inferred from the asymmetric line shape of the thermopower oscillations. The asymmetry is observed at high in-plane magnetic fields and caused by the presence of a high orbital momentum state in the dot.}, author = {Scheibner, R and König, M and Reuter, D and Wieck, A D and Gould, C and Buhmann, H and Molenkamp, L W}, journal = {New Journal of Physics}, keywords = {qt}, number = 8, pages = {083016}, title = {Quantum dot as thermal rectifier}, volume = 10, year = 2008 }

%0 Journal Article %1 scheibner2008quantum %A Scheibner, R %A König, M %A Reuter, D %A Wieck, A D %A Gould, C %A Buhmann, H %A Molenkamp, L W %D 2008 %J New Journal of Physics %N 8 %P 083016 %R 10.1088/1367-2630/10/8/083016 %T Quantum dot as thermal rectifier %V 10 %X We report the observation of thermal rectification in a semiconductor quantum dot, as inferred from the asymmetric line shape of the thermopower oscillations. The asymmetry is observed at high in-plane magnetic fields and caused by the presence of a high orbital momentum state in the dot.

The influence of interfaces and the modulation doping technique on the magneto-transport properties of HgTe based quantum wells. Becker, C.R.; Brüne, C.; Schäfer, M.; Roth, A.H.; Buhmann, H.; Molenkamp, L.W. In Physica Status Solidi C, 4, p. 3382. 2007.
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The influence of interfaces in the structure of HgTe based quantum wells (QW's), their structure as well as the necessary technological processes on their transport properties have been investigated and either reduced or optimized. The mobility (μ) of the 2-dimensional electron gas (2DEG) has been shown to increase when the separation of the 2DEG from the ionized donors is increased, and when the separation of the QW structure from both the insulator on top and the CdTe buffer interface is increased. Furthermore, replacing wet chemical etching in the Hall bar photolithography procedure with a dry plasma etch process resulted in a 2.5 fold increase in the μ. Values for μ up to 0.7 × 10^6 cm^2/(Vs) at 4.2 K have been reproducibly achieved.

@article{becker2007influence, abstract = {The influence of interfaces in the structure of HgTe based quantum wells (QW's), their structure as well as the necessary technological processes on their transport properties have been investigated and either reduced or optimized. The mobility (μ) of the 2-dimensional electron gas (2DEG) has been shown to increase when the separation of the 2DEG from the ionized donors is increased, and when the separation of the QW structure from both the insulator on top and the CdTe buffer interface is increased. Furthermore, replacing wet chemical etching in the Hall bar photolithography procedure with a dry plasma etch process resulted in a 2.5 fold increase in the μ. Values for μ up to 0.7 × 10^6 cm^2/(Vs) at 4.2 K have been reproducibly achieved.}, author = {Becker, C.R. and Brüne, C. and Schäfer, M. and Roth, A.H. and Buhmann, H. and Molenkamp, L.W.}, journal = {Physica Status Solidi C}, keywords = {qt}, month = {06}, pages = 3382, title = {The influence of interfaces and the modulation doping technique on the magneto-transport properties of HgTe based quantum wells}, volume = 4, year = 2007 }

%0 Journal Article %1 becker2007influence %A Becker, C.R. %A Brüne, C. %A Schäfer, M. %A Roth, A.H. %A Buhmann, H. %A Molenkamp, L.W. %D 2007 %J Physica Status Solidi C %P 3382 %R 10.1002/pssc.200775402 %T The influence of interfaces and the modulation doping technique on the magneto-transport properties of HgTe based quantum wells %V 4 %X The influence of interfaces in the structure of HgTe based quantum wells (QW's), their structure as well as the necessary technological processes on their transport properties have been investigated and either reduced or optimized. The mobility (μ) of the 2-dimensional electron gas (2DEG) has been shown to increase when the separation of the 2DEG from the ionized donors is increased, and when the separation of the QW structure from both the insulator on top and the CdTe buffer interface is increased. Furthermore, replacing wet chemical etching in the Hall bar photolithography procedure with a dry plasma etch process resulted in a 2.5 fold increase in the μ. Values for μ up to 0.7 × 10^6 cm^2/(Vs) at 4.2 K have been reproducibly achieved.
Sequential and cotunneling behavior in the temperature-dependent thermopower of few-electron quantum dots. Scheibner, R.; Novik, E. G.; Borzenko, T.; König, M.; Reuter, D.; Wieck, A. D.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 75(4), p. 041301. American Physical Society, 2007.
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We have studied the temperature-dependent thermopower of gate-defined, lateral quantum dots in the Coulomb blockade regime using an electron heating technique. The line shape of the thermopower oscillations depends strongly on the contributing tunneling processes. Between 1.5K and 40mK a crossover from a pure sawtooth to an intermittent sawtoothlike line shape is observed. The latter is attributed to the increasing dominance of cotunneling processes in the Coulomb blockade regime at low temperatures.

@article{scheibner2007sequential, abstract = {We have studied the temperature-dependent thermopower of gate-defined, lateral quantum dots in the Coulomb blockade regime using an electron heating technique. The line shape of the thermopower oscillations depends strongly on the contributing tunneling processes. Between 1.5K and 40mK a crossover from a pure sawtooth to an intermittent sawtoothlike line shape is observed. The latter is attributed to the increasing dominance of cotunneling processes in the Coulomb blockade regime at low temperatures.}, author = {Scheibner, R. and Novik, E. G. and Borzenko, T. and K\"onig, M. and Reuter, D. and Wieck, A. D. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {01}, number = 4, pages = {041301}, publisher = {American Physical Society}, title = {Sequential and cotunneling behavior in the temperature-dependent thermopower of few-electron quantum dots}, volume = 75, year = 2007 }

%0 Journal Article %1 scheibner2007sequential %A Scheibner, R. %A Novik, E. G. %A Borzenko, T. %A König, M. %A Reuter, D. %A Wieck, A. D. %A Buhmann, H. %A Molenkamp, L. W. %D 2007 %I American Physical Society %J Phys. Rev. B %N 4 %P 041301 %R 10.1103/PhysRevB.75.041301 %T Sequential and cotunneling behavior in the temperature-dependent thermopower of few-electron quantum dots %V 75 %X We have studied the temperature-dependent thermopower of gate-defined, lateral quantum dots in the Coulomb blockade regime using an electron heating technique. The line shape of the thermopower oscillations depends strongly on the contributing tunneling processes. Between 1.5K and 40mK a crossover from a pure sawtooth to an intermittent sawtoothlike line shape is observed. The latter is attributed to the increasing dominance of cotunneling processes in the Coulomb blockade regime at low temperatures.
Quantum Spin Hall Insulator State in HgTe Quantum Wells. K{ö}nig, Markus; Wiedmann, Steffen; Br{ü}ne, Christoph; Roth, Andreas; Buhmann, Hartmut; Molenkamp, Laurens W.; Qi, Xiao-Liang; Zhang, Shou-Cheng. In Science, 318(5851), pp. 766–770. American Association for the Advancement of Science, 2007.
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Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e^2/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

@article{konig2007quantum, abstract = {Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e^2/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.}, author = {K{\"o}nig, Markus and Wiedmann, Steffen and Br{\"u}ne, Christoph and Roth, Andreas and Buhmann, Hartmut and Molenkamp, Laurens W. and Qi, Xiao-Liang and Zhang, Shou-Cheng}, journal = {Science}, keywords = {qt}, number = 5851, pages = {766–770}, publisher = {American Association for the Advancement of Science}, title = {Quantum Spin Hall Insulator State in HgTe Quantum Wells}, volume = 318, year = 2007 }

%0 Journal Article %1 konig2007quantum %A K{ö}nig, Markus %A Wiedmann, Steffen %A Br{ü}ne, Christoph %A Roth, Andreas %A Buhmann, Hartmut %A Molenkamp, Laurens W. %A Qi, Xiao-Liang %A Zhang, Shou-Cheng %D 2007 %I American Association for the Advancement of Science %J Science %N 5851 %P 766--770 %R 10.1126/science.1148047 %T Quantum Spin Hall Insulator State in HgTe Quantum Wells %V 318 %X Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e^2/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.
Phase Effects in HgTe Quantum Structures. König, M.; Buhmann, H.; Becker, C.R.; Molenkamp, L.W. In Physica Status Solidi C, 4, p. 3374. 2007.
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HgTe quantum well structures with high electron mobilities have been used to fabricate quantum interference devices. Aharonov-Bohm oscillations have been studied in the low and high magnetic field regime. In the latter case a decrease of the effective ring radius is observed. Additionally, as a consequence of the strong Rashba spin-orbit coupling within this material, it was possible to observe conductance oscillations which are due to the so-called Aharonov-Casher effect. These quantum interference effects are effectively controlled by the applied magnetic and electric field.

@article{knig2007phase, abstract = {HgTe quantum well structures with high electron mobilities have been used to fabricate quantum interference devices. Aharonov-Bohm oscillations have been studied in the low and high magnetic field regime. In the latter case a decrease of the effective ring radius is observed. Additionally, as a consequence of the strong Rashba spin-orbit coupling within this material, it was possible to observe conductance oscillations which are due to the so-called Aharonov-Casher effect. These quantum interference effects are effectively controlled by the applied magnetic and electric field.}, author = {König, M. and Buhmann, H. and Becker, C.R. and Molenkamp, L.W.}, journal = {Physica Status Solidi C}, keywords = {qt}, month = {08}, pages = 3374, title = {Phase Effects in HgTe Quantum Structures}, volume = 4, year = 2007 }

%0 Journal Article %1 knig2007phase %A König, M. %A Buhmann, H. %A Becker, C.R. %A Molenkamp, L.W. %D 2007 %J Physica Status Solidi C %P 3374 %R 10.1002/pssc.200775420 %T Phase Effects in HgTe Quantum Structures %V 4 %X HgTe quantum well structures with high electron mobilities have been used to fabricate quantum interference devices. Aharonov-Bohm oscillations have been studied in the low and high magnetic field regime. In the latter case a decrease of the effective ring radius is observed. Additionally, as a consequence of the strong Rashba spin-orbit coupling within this material, it was possible to observe conductance oscillations which are due to the so-called Aharonov-Casher effect. These quantum interference effects are effectively controlled by the applied magnetic and electric field.

Gate control of the giant Rashba effect in HgTe quantum wells. Hinz, J.; Buhmann, H.; Schäfer, M.; Hock, V.; Becker, C.R.; Molenkamp, L.W. In Semiconductor Science and Technology, 21(4), p. 501. 2006.
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HgTe/Hg 0.3 Cd 0.7 Te(0 0 1) quantum well structures fabricated with a Si–O–N insulator layer and an Au top gate electrode exhibit hysteresis effects in their gate-voltage dependent carrier density and thus a nonlinear variation of the Rashba spin–orbit splitting energy (Δ R ). Charging and discharging of states at the semiconductor insulator interface has been found to be responsible for this effect. The quantitative agreement with a simple capacitor model has been used to identify the maximum hysteresis-free gate-voltage range. A nearly linear variation of Δ R with applied gate voltage has been observed in this range.

@article{hinz2006control, abstract = {HgTe/Hg 0.3 Cd 0.7 Te(0 0 1) quantum well structures fabricated with a Si–O–N insulator layer and an Au top gate electrode exhibit hysteresis effects in their gate-voltage dependent carrier density and thus a nonlinear variation of the Rashba spin–orbit splitting energy (Δ R ). Charging and discharging of states at the semiconductor insulator interface has been found to be responsible for this effect. The quantitative agreement with a simple capacitor model has been used to identify the maximum hysteresis-free gate-voltage range. A nearly linear variation of Δ R with applied gate voltage has been observed in this range.}, author = {Hinz, J. and Buhmann, H. and Schäfer, M. and Hock, V. and Becker, C.R. and Molenkamp, L.W.}, journal = {Semiconductor Science and Technology}, keywords = {qt}, number = 4, pages = 501, title = {Gate control of the giant Rashba effect in HgTe quantum wells}, volume = 21, year = 2006 }

%0 Journal Article %1 hinz2006control %A Hinz, J. %A Buhmann, H. %A Schäfer, M. %A Hock, V. %A Becker, C.R. %A Molenkamp, L.W. %D 2006 %J Semiconductor Science and Technology %N 4 %P 501 %R 10.1088/0268-1242/21/4/015 %T Gate control of the giant Rashba effect in HgTe quantum wells %V 21 %X HgTe/Hg 0.3 Cd 0.7 Te(0 0 1) quantum well structures fabricated with a Si–O–N insulator layer and an Au top gate electrode exhibit hysteresis effects in their gate-voltage dependent carrier density and thus a nonlinear variation of the Rashba spin–orbit splitting energy (Δ R ). Charging and discharging of states at the semiconductor insulator interface has been found to be responsible for this effect. The quantitative agreement with a simple capacitor model has been used to identify the maximum hysteresis-free gate-voltage range. A nearly linear variation of Δ R with applied gate voltage has been observed in this range.
Exchange Interaction in Magnetic HgMnTe-Quantum Well Structures. Liu, J.; Buhmann, H.; Novik, E.G.; Gui, Y.S.; Hock, V.; Becker, C.R.; Molenkamp, L.W. In Physica Status Solidi B, 243, p. 835. 2006.
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Low temperature magnetotransport measurements have been used to study the exchange interactions in Hg(1–x)Mn(x)Te magnetic quantum wells (QWs). An analysis of Shubnikov–de Haas oscillations in conjunction with 8 × 8 k · p bandstructure calculations allow the exchange constants N0α and N0β , the antiferromagnetic temperature T0, and the effective spin S0 to be determined. The latter displays a distinct temperature dependence and appears to be enhanced compared with bulk materials of equivalent Mn concentrations.

@article{liu2006exchange, abstract = {Low temperature magnetotransport measurements have been used to study the exchange interactions in Hg(1–x)Mn(x)Te magnetic quantum wells (QWs). An analysis of Shubnikov–de Haas oscillations in conjunction with 8 × 8 k · p bandstructure calculations allow the exchange constants N0α and N0β , the antiferromagnetic temperature T0, and the effective spin S0 to be determined. The latter displays a distinct temperature dependence and appears to be enhanced compared with bulk materials of equivalent Mn concentrations.}, author = {Liu, J. and Buhmann, H. and Novik, E.G. and Gui, Y.S. and Hock, V. and Becker, C.R. and Molenkamp, L.W.}, journal = {Physica Status Solidi B}, keywords = {qt}, month = {03}, pages = 835, title = {Exchange Interaction in Magnetic HgMnTe-Quantum Well Structures}, volume = 243, year = 2006 }

%0 Journal Article %1 liu2006exchange %A Liu, J. %A Buhmann, H. %A Novik, E.G. %A Gui, Y.S. %A Hock, V. %A Becker, C.R. %A Molenkamp, L.W. %D 2006 %J Physica Status Solidi B %P 835 %R 10.1002/pssb.200564610 %T Exchange Interaction in Magnetic HgMnTe-Quantum Well Structures %V 243 %X Low temperature magnetotransport measurements have been used to study the exchange interactions in Hg(1–x)Mn(x)Te magnetic quantum wells (QWs). An analysis of Shubnikov–de Haas oscillations in conjunction with 8 × 8 k · p bandstructure calculations allow the exchange constants N0α and N0β , the antiferromagnetic temperature T0, and the effective spin S0 to be determined. The latter displays a distinct temperature dependence and appears to be enhanced compared with bulk materials of equivalent Mn concentrations.
Direct Observation of the Aharonov-Casher Phase. König, M.; Tschetschetkin, A.; Hankiewicz, E. M.; Sinova, Jairo; Hock, V.; Daumer, V.; Schäfer, M.; Becker, C. R.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Lett., 96(7), p. 076804. American Physical Society, 2006.
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Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.

@article{konig2006direct, abstract = {Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.}, author = {K\"onig, M. and Tschetschetkin, A. and Hankiewicz, E. M. and Sinova, Jairo and Hock, V. and Daumer, V. and Sch\"afer, M. and Becker, C. R. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {02}, number = 7, pages = {076804}, publisher = {American Physical Society}, title = {Direct Observation of the Aharonov-Casher Phase}, volume = 96, year = 2006 }

%0 Journal Article %1 konig2006direct %A König, M. %A Tschetschetkin, A. %A Hankiewicz, E. M. %A Sinova, Jairo %A Hock, V. %A Daumer, V. %A Schäfer, M. %A Becker, C. R. %A Buhmann, H. %A Molenkamp, L. W. %D 2006 %I American Physical Society %J Phys. Rev. Lett. %N 7 %P 076804 %R 10.1103/PhysRevLett.96.076804 %T Direct Observation of the Aharonov-Casher Phase %V 96 %X Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.

Trion formation in narrow GaAs quantum well structures. Teran, F. J.; Eaves, L.; Mansouri, L.; Buhmann, H.; Maude, D. K.; Potemski, M.; Henini, M.; Hill, G. In Phys. Rev. B, 71(16), p. 161309. American Physical Society, 2005.
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We study the optical and electrical properties of n−i−n GaAs∕AlAs double-barrier resonant tunneling diodes. Under illumination, new resonances appear in the current-voltage curves due to tunneling of photoexcited holes. By tuning the bias and the intensity of illumination, we can control independently the number of electrons and holes tunneling into the quantum well. This allows us to create charge conditions in the well that favor the formation of either positively charged, neutral, or negatively charged excitons. Our measured value of the binding energy of the second electron in the negative trion is significantly larger than that of the second hole in the positive trion.

@article{teran2005trion, abstract = {We study the optical and electrical properties of n−i−n GaAs∕AlAs double-barrier resonant tunneling diodes. Under illumination, new resonances appear in the current-voltage curves due to tunneling of photoexcited holes. By tuning the bias and the intensity of illumination, we can control independently the number of electrons and holes tunneling into the quantum well. This allows us to create charge conditions in the well that favor the formation of either positively charged, neutral, or negatively charged excitons. Our measured value of the binding energy of the second electron in the negative trion is significantly larger than that of the second hole in the positive trion.}, author = {Teran, F. J. and Eaves, L. and Mansouri, L. and Buhmann, H. and Maude, D. K. and Potemski, M. and Henini, M. and Hill, G.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {04}, number = 16, pages = 161309, publisher = {American Physical Society}, title = {Trion formation in narrow GaAs quantum well structures}, volume = 71, year = 2005 }

%0 Journal Article %1 teran2005trion %A Teran, F. J. %A Eaves, L. %A Mansouri, L. %A Buhmann, H. %A Maude, D. K. %A Potemski, M. %A Henini, M. %A Hill, G. %D 2005 %I American Physical Society %J Phys. Rev. B %N 16 %P 161309 %R 10.1103/PhysRevB.71.161309 %T Trion formation in narrow GaAs quantum well structures %V 71 %X We study the optical and electrical properties of n−i−n GaAs∕AlAs double-barrier resonant tunneling diodes. Under illumination, new resonances appear in the current-voltage curves due to tunneling of photoexcited holes. By tuning the bias and the intensity of illumination, we can control independently the number of electrons and holes tunneling into the quantum well. This allows us to create charge conditions in the well that favor the formation of either positively charged, neutral, or negatively charged excitons. Our measured value of the binding energy of the second electron in the negative trion is significantly larger than that of the second hole in the positive trion.
Thermopower of a Kondo Spin-Correlated Quantum Dot. Scheibner, R.; Buhmann, H.; Reuter, D.; Kiselev, M. N.; Molenkamp, L. W. In Phys. Rev. Lett., 95(17), p. 176602. American Physical Society, 2005.
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The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations, the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model.

@article{scheibner2005thermopower, abstract = {The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations, the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model.}, author = {Scheibner, R. and Buhmann, H. and Reuter, D. and Kiselev, M. N. and Molenkamp, L. W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = 10, number = 17, pages = 176602, publisher = {American Physical Society}, title = {Thermopower of a Kondo Spin-Correlated Quantum Dot}, volume = 95, year = 2005 }

%0 Journal Article %1 scheibner2005thermopower %A Scheibner, R. %A Buhmann, H. %A Reuter, D. %A Kiselev, M. N. %A Molenkamp, L. W. %D 2005 %I American Physical Society %J Phys. Rev. Lett. %N 17 %P 176602 %R 10.1103/PhysRevLett.95.176602 %T Thermopower of a Kondo Spin-Correlated Quantum Dot %V 95 %X The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations, the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model.
Odd filling factor quantum Hall sequence in magnetic type-III quantum wells. Buhmann, H.; Novik, E. G.; Daumer, V.; Liu, J.; Gui, Y. S.; Becker, C. R.; Molenkamp, L. W. In Appl. Phys. Lett., 86(21), p. 212104. American Institute of Physics, 2005.
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The magnetotransport properties of a series of Hg(1−y)Mn(y)Te quantum wells (y=2%) reveal anomalous sequences of quantum Hall plateaus and corresponding minima in the longitudinal magnetoresistance which correspond solely to odd filling factors. This anomaly originates from the very large spin splitting in this material, which exceeds the cyclotron energy even at moderate magnetic fields (B>2T). An 8×8 band k∙p approach has been used to calculate the magnetic field dependence of the Landau levels. Finite temperature and Landau level broadening considerations confirm that subband crossings in the vicinity of the Fermi energy are responsible for the suppression of even filling factor quantum Hall states.

@article{buhmann2005filling, abstract = {The magnetotransport properties of a series of Hg(1−y)Mn(y)Te quantum wells (y=2%) reveal anomalous sequences of quantum Hall plateaus and corresponding minima in the longitudinal magnetoresistance which correspond solely to odd filling factors. This anomaly originates from the very large spin splitting in this material, which exceeds the cyclotron energy even at moderate magnetic fields (B>2T). An 8×8 band k∙p approach has been used to calculate the magnetic field dependence of the Landau levels. Finite temperature and Landau level broadening considerations confirm that subband crossings in the vicinity of the Fermi energy are responsible for the suppression of even filling factor quantum Hall states.}, author = {Buhmann, H. and Novik, E. G. and Daumer, V. and Liu, J. and Gui, Y. S. and Becker, C. R. and Molenkamp, L. W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {05}, number = 21, pages = 212104, publisher = {American Institute of Physics}, title = {Odd filling factor quantum Hall sequence in magnetic type-III quantum wells}, volume = 86, year = 2005 }

%0 Journal Article %1 buhmann2005filling %A Buhmann, H. %A Novik, E. G. %A Daumer, V. %A Liu, J. %A Gui, Y. S. %A Becker, C. R. %A Molenkamp, L. W. %B Applied Physics Letters %D 2005 %I American Institute of Physics %J Appl. Phys. Lett. %N 21 %P 212104 %R 10.1063/1.1935753 %T Odd filling factor quantum Hall sequence in magnetic type-III quantum wells %V 86 %X The magnetotransport properties of a series of Hg(1−y)Mn(y)Te quantum wells (y=2%) reveal anomalous sequences of quantum Hall plateaus and corresponding minima in the longitudinal magnetoresistance which correspond solely to odd filling factors. This anomaly originates from the very large spin splitting in this material, which exceeds the cyclotron energy even at moderate magnetic fields (B>2T). An 8×8 band k∙p approach has been used to calculate the magnetic field dependence of the Landau levels. Finite temperature and Landau level broadening considerations confirm that subband crossings in the vicinity of the Fermi energy are responsible for the suppression of even filling factor quantum Hall states.
Band structure of semimagnetic Hg(1-y)Mn(y)Te quantum wells. Novik, E. G.; Pfeuffer-Jeschke, A.; Jungwirth, T.; Latussek, V.; Becker, C. R.; Landwehr, G.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 72(3), p. 035321. American Physical Society, 2005.
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The band structure of semimagnetic Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te type-III quantum wells (QW’s) has been calculated using an eight-band k∙p model in an envelope function approach. Details of the band structure calculations are given for the Mn-free case (y=0). A mean-field approach is used to take the influence of the sp−d exchange interaction on the band structure of QW’s with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the sp−d exchange interaction on the transport properties of Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te QW’s.

@article{novik2005structure, abstract = {The band structure of semimagnetic Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te type-III quantum wells (QW’s) has been calculated using an eight-band k∙p model in an envelope function approach. Details of the band structure calculations are given for the Mn-free case (y=0). A mean-field approach is used to take the influence of the sp−d exchange interaction on the band structure of QW’s with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the sp−d exchange interaction on the transport properties of Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te QW’s.}, author = {Novik, E. G. and Pfeuffer-Jeschke, A. and Jungwirth, T. and Latussek, V. and Becker, C. R. and Landwehr, G. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {07}, number = 3, pages = {035321}, publisher = {American Physical Society}, title = {Band structure of semimagnetic Hg(1-y)Mn(y)Te quantum wells}, volume = 72, year = 2005 }

%0 Journal Article %1 novik2005structure %A Novik, E. G. %A Pfeuffer-Jeschke, A. %A Jungwirth, T. %A Latussek, V. %A Becker, C. R. %A Landwehr, G. %A Buhmann, H. %A Molenkamp, L. W. %D 2005 %I American Physical Society %J Phys. Rev. B %N 3 %P 035321 %R 10.1103/PhysRevB.72.035321 %T Band structure of semimagnetic Hg(1-y)Mn(y)Te quantum wells %V 72 %X The band structure of semimagnetic Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te type-III quantum wells (QW’s) has been calculated using an eight-band k∙p model in an envelope function approach. Details of the band structure calculations are given for the Mn-free case (y=0). A mean-field approach is used to take the influence of the sp−d exchange interaction on the band structure of QW’s with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the sp−d exchange interaction on the transport properties of Hg(1−y)Mn(y)Te/Hg(1−x)Cd(x)Te QW’s.

Low-field diffusion magnetothermopower of a high-mobility two-dimensional electron gas. Maximov, S.; Gbordzoe, M.; Buhmann, H.; Molenkamp, L. W.; Reuter, D. In Phys. Rev. B, 70(12), p. 121308. American Physical Society, 2004.
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The low-magnetic field-diffusion thermopower of a high-mobility GaAs heterostructure has been measured directly on an electrostatically defined micron-scale Hall-bar structure (4μm×8μm) at low temperature (T=1.6K) in the field regime (B⩽1.2T) where the formation of edge states does not influence the measurements. The sample design allowed the determination of the field dependence of the thermopower both parallel and perpendicular to the temperature gradient, denoted respectively by Sxx (longitudinal thermopower) and Syx (the Nernst-Ettinghausen coefficient). The experimental data show clear oscillations in Sxx and Syx due to the formation of Landau levels and reveal that Syx≈120Sxx at a magnetic field of 1T, which agrees well with the theoretical prediction that the ratio of these tensor components is dependent on the carrier mobility: Syx/Sxx=2ωcτ.

@article{maximov2004lowfield, abstract = {The low-magnetic field-diffusion thermopower of a high-mobility GaAs heterostructure has been measured directly on an electrostatically defined micron-scale Hall-bar structure (4μm×8μm) at low temperature (T=1.6K) in the field regime (B⩽1.2T) where the formation of edge states does not influence the measurements. The sample design allowed the determination of the field dependence of the thermopower both parallel and perpendicular to the temperature gradient, denoted respectively by Sxx (longitudinal thermopower) and Syx (the Nernst-Ettinghausen coefficient). The experimental data show clear oscillations in Sxx and Syx due to the formation of Landau levels and reveal that Syx≈120Sxx at a magnetic field of 1T, which agrees well with the theoretical prediction that the ratio of these tensor components is dependent on the carrier mobility: Syx/Sxx=2ωcτ.}, author = {Maximov, S. and Gbordzoe, M. and Buhmann, H. and Molenkamp, L. W. and Reuter, D.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {09}, number = 12, pages = 121308, publisher = {American Physical Society}, title = {Low-field diffusion magnetothermopower of a high-mobility two-dimensional electron gas}, volume = 70, year = 2004 }

%0 Journal Article %1 maximov2004lowfield %A Maximov, S. %A Gbordzoe, M. %A Buhmann, H. %A Molenkamp, L. W. %A Reuter, D. %D 2004 %I American Physical Society %J Phys. Rev. B %N 12 %P 121308 %R 10.1103/PhysRevB.70.121308 %T Low-field diffusion magnetothermopower of a high-mobility two-dimensional electron gas %V 70 %X The low-magnetic field-diffusion thermopower of a high-mobility GaAs heterostructure has been measured directly on an electrostatically defined micron-scale Hall-bar structure (4μm×8μm) at low temperature (T=1.6K) in the field regime (B⩽1.2T) where the formation of edge states does not influence the measurements. The sample design allowed the determination of the field dependence of the thermopower both parallel and perpendicular to the temperature gradient, denoted respectively by Sxx (longitudinal thermopower) and Syx (the Nernst-Ettinghausen coefficient). The experimental data show clear oscillations in Sxx and Syx due to the formation of Landau levels and reveal that Syx≈120Sxx at a magnetic field of 1T, which agrees well with the theoretical prediction that the ratio of these tensor components is dependent on the carrier mobility: Syx/Sxx=2ωcτ.
Interplay of Rashba, Zeeman and Landau splitting in a magnetic two dimensional electron gas. Gui, Y.S.; Becker, C.R.; Liu, J.; Daumer, V.; Hock, V.; Buhmann, H.; Molenkamp, L.W. In Europhys. Lett., 65(3), p. 393. 2004.
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The transport properties of a magnetic two-dimensional electron gas consisting of a modulation doped n-type Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te quantum well, QW, have been investigated. By analyzing the Shubnikov-de Haas oscillations and the node positions of their beating patterns, we have been able to separate the gate-voltage-dependent Rashba spin-orbit splitting from the temperature-dependent giant Zeeman splitting. It has been experimentally demonstrated that the Rashba spin-orbit splitting is larger than or comparable to the sp-d exchange-interaction–induced giant Zeeman splitting in this magnetic 2DEG even at moderately high magnetic fields.

@article{gui2004interplay, abstract = {The transport properties of a magnetic two-dimensional electron gas consisting of a modulation doped n-type Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te quantum well, QW, have been investigated. By analyzing the Shubnikov-de Haas oscillations and the node positions of their beating patterns, we have been able to separate the gate-voltage-dependent Rashba spin-orbit splitting from the temperature-dependent giant Zeeman splitting. It has been experimentally demonstrated that the Rashba spin-orbit splitting is larger than or comparable to the sp-d exchange-interaction–induced giant Zeeman splitting in this magnetic 2DEG even at moderately high magnetic fields.}, author = {Gui, Y.S. and Becker, C.R. and Liu, J. and Daumer, V. and Hock, V. and Buhmann, H. and Molenkamp, L.W.}, journal = {Europhys. Lett.}, keywords = {qt}, number = 3, pages = 393, title = {Interplay of Rashba, Zeeman and Landau splitting in a magnetic two dimensional electron gas}, volume = 65, year = 2004 }

%0 Journal Article %1 gui2004interplay %A Gui, Y.S. %A Becker, C.R. %A Liu, J. %A Daumer, V. %A Hock, V. %A Buhmann, H. %A Molenkamp, L.W. %D 2004 %J Europhys. Lett. %N 3 %P 393 %R 10.1209/epl/i2003-10094-2 %T Interplay of Rashba, Zeeman and Landau splitting in a magnetic two dimensional electron gas %V 65 %X The transport properties of a magnetic two-dimensional electron gas consisting of a modulation doped n-type Hg(0.98)Mn(0.02)Te/Hg(0.3)Cd(0.7)Te quantum well, QW, have been investigated. By analyzing the Shubnikov-de Haas oscillations and the node positions of their beating patterns, we have been able to separate the gate-voltage-dependent Rashba spin-orbit splitting from the temperature-dependent giant Zeeman splitting. It has been experimentally demonstrated that the Rashba spin-orbit splitting is larger than or comparable to the sp-d exchange-interaction–induced giant Zeeman splitting in this magnetic 2DEG even at moderately high magnetic fields.
Growth and studies of Hg(1-x)Cd(x)Te based low dimensional structures. Becker, C.R.; Ortner, K.; Zhang, X.C.; Pfeuffer-Jeschke, A.; Latussek, V.; Gui, Y.S.; Daumer, V.; Buhmann, H.; Landwehr, G.; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 20(3-4), pp. 436–443. Elsevier {BV}, 2004.
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The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8x8 k p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained. Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV. By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg(1−x)Mn(x)Te QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current. Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.

@article{becker2004growth, abstract = {The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8x8 k p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained. Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV. By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg(1−x)Mn(x)Te QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current. Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.}, author = {Becker, C.R. and Ortner, K. and Zhang, X.C. and Pfeuffer-Jeschke, A. and Latussek, V. and Gui, Y.S. and Daumer, V. and Buhmann, H. and Landwehr, G. and Molenkamp, L.W.}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {01}, number = {3-4}, pages = {436–443}, publisher = {Elsevier {BV}}, title = {Growth and studies of Hg(1-x)Cd(x)Te based low dimensional structures}, volume = 20, year = 2004 }

%0 Journal Article %1 becker2004growth %A Becker, C.R. %A Ortner, K. %A Zhang, X.C. %A Pfeuffer-Jeschke, A. %A Latussek, V. %A Gui, Y.S. %A Daumer, V. %A Buhmann, H. %A Landwehr, G. %A Molenkamp, L.W. %D 2004 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 3-4 %P 436--443 %R 10.1016/j.physe.2003.08.053 %T Growth and studies of Hg(1-x)Cd(x)Te based low dimensional structures %V 20 %X The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8x8 k p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained. Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV. By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg(1−x)Mn(x)Te QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current. Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.
Giant spin-orbit splitting in a HgTe quantum well. Gui, Y. S.; Becker, C. R.; Dai, N.; Liu, J.; Qiu, Z. J.; Novik, E. G.; Schäfer, M.; Shu, X. Z.; Chu, J. H.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 70(11), p. 115328. American Physical Society, 2004.
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We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te (001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.

@article{gui2004giant, abstract = {We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te (001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.}, author = {Gui, Y. S. and Becker, C. R. and Dai, N. and Liu, J. and Qiu, Z. J. and Novik, E. G. and Sch\"afer, M. and Shu, X. Z. and Chu, J. H. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {09}, number = 11, pages = 115328, publisher = {American Physical Society}, title = {Giant spin-orbit splitting in a HgTe quantum well}, volume = 70, year = 2004 }

%0 Journal Article %1 gui2004giant %A Gui, Y. S. %A Becker, C. R. %A Dai, N. %A Liu, J. %A Qiu, Z. J. %A Novik, E. G. %A Schäfer, M. %A Shu, X. Z. %A Chu, J. H. %A Buhmann, H. %A Molenkamp, L. W. %D 2004 %I American Physical Society %J Phys. Rev. B %N 11 %P 115328 %R 10.1103/PhysRevB.70.115328 %T Giant spin-orbit splitting in a HgTe quantum well %V 70 %X We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te (001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.
Current heating of a magnetic two-dimensional electron gas in Hg(1-x)Mn(x)Te∕Hg(0.3)Cd(0.7)Te quantum wells. Gui, Y. S.; Becker, C. R.; Liu, J.; König, M.; Daumer, V.; Kiselev, M. N.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 70(19), p. 195328. American Physical Society, 2004.
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Heating caused by electrons with excess kinetic energy has been investigated in a magnetic two-dimensional electron gas in Hg(1−x)Mn(x)Te/Hg(0.3)Cd(0.7)Te (001) quantum wells. The temperature of the Mn ions T_Mn has been determined by the node positions in the beating pattern in Shubnikov–de Haas oscillations. The experimental dependence of T_Mn on current and therefore on electron temperature, is in excellent agreement with a rate equation model.

@article{gui2004current, abstract = {Heating caused by electrons with excess kinetic energy has been investigated in a magnetic two-dimensional electron gas in Hg(1−x)Mn(x)Te/Hg(0.3)Cd(0.7)Te (001) quantum wells. The temperature of the Mn ions T_Mn has been determined by the node positions in the beating pattern in Shubnikov–de Haas oscillations. The experimental dependence of T_Mn on current and therefore on electron temperature, is in excellent agreement with a rate equation model.}, author = {Gui, Y. S. and Becker, C. R. and Liu, J. and K\"onig, M. and Daumer, V. and Kiselev, M. N. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 11, number = 19, pages = 195328, publisher = {American Physical Society}, title = {Current heating of a magnetic two-dimensional electron gas in Hg(1-x)Mn(x)Te∕Hg(0.3)Cd(0.7)Te quantum wells}, volume = 70, year = 2004 }

%0 Journal Article %1 gui2004current %A Gui, Y. S. %A Becker, C. R. %A Liu, J. %A König, M. %A Daumer, V. %A Kiselev, M. N. %A Buhmann, H. %A Molenkamp, L. W. %D 2004 %I American Physical Society %J Phys. Rev. B %N 19 %P 195328 %R 10.1103/PhysRevB.70.195328 %T Current heating of a magnetic two-dimensional electron gas in Hg(1-x)Mn(x)Te∕Hg(0.3)Cd(0.7)Te quantum wells %V 70 %X Heating caused by electrons with excess kinetic energy has been investigated in a magnetic two-dimensional electron gas in Hg(1−x)Mn(x)Te/Hg(0.3)Cd(0.7)Te (001) quantum wells. The temperature of the Mn ions T_Mn has been determined by the node positions in the beating pattern in Shubnikov–de Haas oscillations. The experimental dependence of T_Mn on current and therefore on electron temperature, is in excellent agreement with a rate equation model.

Relaxation of high-energy quasiparticle distributions: Electron-electron scattering in a two-dimensional electron gas. Gurzhi, R. N.; Kopeliovich, A. I.; Kalinenko, A. N.; Yanovsky, A. V.; Bogachek, E. N.; Landman, Uzi; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 68(16), p. 165318. American Physical Society, 2003.
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We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te(001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.

@article{gurzhi2003relaxation, abstract = {We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te(001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.}, author = {Gurzhi, R. N. and Kopeliovich, A. I. and Kalinenko, A. N. and Yanovsky, A. V. and Bogachek, E. N. and Landman, Uzi and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = 10, number = 16, pages = 165318, publisher = {American Physical Society}, title = {Relaxation of high-energy quasiparticle distributions: Electron-electron scattering in a two-dimensional electron gas}, volume = 68, year = 2003 }

%0 Journal Article %1 gurzhi2003relaxation %A Gurzhi, R. N. %A Kopeliovich, A. I. %A Kalinenko, A. N. %A Yanovsky, A. V. %A Bogachek, E. N. %A Landman, Uzi %A Buhmann, H. %A Molenkamp, L. W. %D 2003 %I American Physical Society %J Phys. Rev. B %N 16 %P 165318 %R 10.1103/PhysRevB.68.165318 %T Relaxation of high-energy quasiparticle distributions: Electron-electron scattering in a two-dimensional electron gas %V 68 %X We have investigated beating patterns in Shubnikov–de Haas oscillations for HgTe/Hg(0.3)Cd(0.7)Te(001) quantum wells with electron densities of 2–3×10^12cm^−2. Up to 12 beating nodes have been observed at magnetic fields between 0.9 and 6T. Zero-magnetic-field spin-orbit splitting energies up to 30meV have been directly determined from the node positions as well as from the intersection of self-consistently calculated Landau levels. These values, which exceed the thermal broadening of Landau levels, kBT, at room temperature, are in good agreement with Rashba spin-orbit splitting energies calculated by means of an 8×8k∙p Kane model. The experimental Shubnikov–de Haas oscillations are also in good agreement with numerical simulations based on this model.
Quasiballistic transport in HgTe quantum-well nanostructures. Daumer, V; Golombek, I; Gbordzoe, M; Novik, E. G.; Hock, V; Becker, C. R.; Buhmann, H; Molenkamp, L. W. In Appl. Phys. Lett., 83(7), pp. 1376–1378. American Institute of Physics, 2003.
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The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 μm. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semiclassical electron trajectories show good agreement with the experiment.

@article{daumer2003quasiballistic, abstract = {The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 μm. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semiclassical electron trajectories show good agreement with the experiment.}, author = {Daumer, V and Golombek, I and Gbordzoe, M and Novik, E. G. and Hock, V and Becker, C. R. and Buhmann, H and Molenkamp, L. W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {08}, number = 7, pages = {1376–1378}, publisher = {American Institute of Physics}, title = {Quasiballistic transport in HgTe quantum-well nanostructures}, volume = 83, year = 2003 }

%0 Journal Article %1 daumer2003quasiballistic %A Daumer, V %A Golombek, I %A Gbordzoe, M %A Novik, E. G. %A Hock, V %A Becker, C. R. %A Buhmann, H %A Molenkamp, L. W. %B Applied Physics Letters %D 2003 %I American Institute of Physics %J Appl. Phys. Lett. %N 7 %P 1376--1378 %R 10.1063/1.1602170 %T Quasiballistic transport in HgTe quantum-well nanostructures %V 83 %X The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 μm. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semiclassical electron trajectories show good agreement with the experiment.
Electron-beam propagation in a two-dimensional electron gas. Novik, E. G.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 67(24), p. 245302. American Physical Society, 2003.
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A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.

@article{novik2003electronbeam, abstract = {A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.}, author = {Novik, E. G. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {06}, number = 24, pages = 245302, publisher = {American Physical Society}, title = {Electron-beam propagation in a two-dimensional electron gas}, volume = 67, year = 2003 }

%0 Journal Article %1 novik2003electronbeam %A Novik, E. G. %A Buhmann, H. %A Molenkamp, L. W. %D 2003 %I American Physical Society %J Phys. Rev. B %N 24 %P 245302 %R 10.1103/PhysRevB.67.245302 %T Electron-beam propagation in a two-dimensional electron gas %V 67 %X A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.
Competition Between Rashba Effect and Exchange Interaction in a Hg(0.98)Mn(0.02)Te Magnetic 2DEG. Liu, J.; Daumer, V.; Gui, Y. S.; Hock, V.; Becker, C. R.; Buhmann, H.; Molenkamp, L. W. In Journal of Superconductivity, 16(2), pp. 365–368. 2003.
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Magnetotransport measurements are used to study the peculiar properties of a modulation doped n-type Hg(0.98)Mn(0.02)Te magnetic 2DEG. The Rashba effect and giant Zeeman spin splitting are observed simultaneously and can be separated by temperature and gate voltage dependent Shubnikov-de Haas oscillations. The Rashba effect is found to be the dominant term up to 5 T.

@article{liu2003competition, abstract = {Magnetotransport measurements are used to study the peculiar properties of a modulation doped n-type Hg(0.98)Mn(0.02)Te magnetic 2DEG. The Rashba effect and giant Zeeman spin splitting are observed simultaneously and can be separated by temperature and gate voltage dependent Shubnikov-de Haas oscillations. The Rashba effect is found to be the dominant term up to 5 T.}, author = {Liu, J. and Daumer, V. and Gui, Y. S. and Hock, V. and Becker, C. R. and Buhmann, H. and Molenkamp, L. W.}, journal = {Journal of Superconductivity}, keywords = {qt}, month = {04}, number = 2, pages = {365–368}, title = {Competition Between Rashba Effect and Exchange Interaction in a Hg(0.98)Mn(0.02)Te Magnetic 2DEG}, volume = 16, year = 2003 }

%0 Journal Article %1 liu2003competition %A Liu, J. %A Daumer, V. %A Gui, Y. S. %A Hock, V. %A Becker, C. R. %A Buhmann, H. %A Molenkamp, L. W. %D 2003 %J Journal of Superconductivity %N 2 %P 365--368 %R 10.1023/A:1023638125071 %T Competition Between Rashba Effect and Exchange Interaction in a Hg(0.98)Mn(0.02)Te Magnetic 2DEG %V 16 %X Magnetotransport measurements are used to study the peculiar properties of a modulation doped n-type Hg(0.98)Mn(0.02)Te magnetic 2DEG. The Rashba effect and giant Zeeman spin splitting are observed simultaneously and can be separated by temperature and gate voltage dependent Shubnikov-de Haas oscillations. The Rashba effect is found to be the dominant term up to 5 T.

Spectroscopical imaging of electron scattering in two-dimensional conductors. Yanovsky, A.V.; Predel, H.; Buhmann, H.; Gurzhi, R.N.; Kalinenko, A.N.; Kopeliovich, A.I.; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 12(1-4), pp. 241–243. Elsevier {BV}, 2002.
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A new method to study electron scattering processes in conductors is proposed and experimentally realized. This method is based on the separation of the particles which are scattered at the different angles in a magnetic field. Experimental implementation of this method on GaAs(AlGaAs) heterojunctions has confirmed the ideas about essential differences of momentum transfer mechanisms in two- and three-dimensional systems. Most conspicuous is the increased importance of the small angular scattering for small excess energies.

@article{yanovsky2002spectroscopical, abstract = {A new method to study electron scattering processes in conductors is proposed and experimentally realized. This method is based on the separation of the particles which are scattered at the different angles in a magnetic field. Experimental implementation of this method on GaAs(AlGaAs) heterojunctions has confirmed the ideas about essential differences of momentum transfer mechanisms in two- and three-dimensional systems. Most conspicuous is the increased importance of the small angular scattering for small excess energies.}, author = {Yanovsky, A.V. and Predel, H. and Buhmann, H. and Gurzhi, R.N. and Kalinenko, A.N. and Kopeliovich, A.I. and Molenkamp, L.W.}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {01}, number = {1-4}, pages = {241–243}, publisher = {Elsevier {BV}}, title = {Spectroscopical imaging of electron scattering in two-dimensional conductors}, volume = 12, year = 2002 }

%0 Journal Article %1 yanovsky2002spectroscopical %A Yanovsky, A.V. %A Predel, H. %A Buhmann, H. %A Gurzhi, R.N. %A Kalinenko, A.N. %A Kopeliovich, A.I. %A Molenkamp, L.W. %D 2002 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 241--243 %R 10.1016/s1386-9477(01)00363-0 %T Spectroscopical imaging of electron scattering in two-dimensional conductors %V 12 %X A new method to study electron scattering processes in conductors is proposed and experimentally realized. This method is based on the separation of the particles which are scattered at the different angles in a magnetic field. Experimental implementation of this method on GaAs(AlGaAs) heterojunctions has confirmed the ideas about essential differences of momentum transfer mechanisms in two- and three-dimensional systems. Most conspicuous is the increased importance of the small angular scattering for small excess energies.
{MBE} growth and characterization of Hg based compounds and heterostructures. Becker, C.R; Zhang, X.C; Ortner, K; Schmidt, J; Pfeuffer-Jeschke, A; Latussek, V; Gui, Y.S; Daumer, V; Liu, J; Buhmann, H; Landwehr, G; Molenkamp, L.W. In Thin Solid Films, 412(1-2), pp. 129–138. Elsevier {BV}, 2002.
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The MBE growth of Hg(1−x)Cd(x)Te alloys and type III HgTe/Hg(1−x)Cd(x)Te heterostructures has been discussed, including similarities and differences between the (0 0 1) and (1 1 2)B orientations. Furthermore the MBE growth of HgTe based quantum wells (QWs) with the incorporation of Mn are additional topics. An investigation of the optical properties of type III superlattices with a normal band structure has lead to information about band structure of these heterostructures as well as information about the interface and the semimetallic QW. For example, by means of the full 8×8 Kane Hamiltonian in the envelope function approximation, it has been demonstrated that the energy separation between the H1–E1 and L1–E1 intersubband transition energies is primarily determined by the valence band offset, Λ, between HgTe and CdTe. This has led to unambiguous values for the offset and its temperature dependence, i.e. Λ(T)=570±60 meV and dΛ/dT=−0.40±0.04T meV/K. Furthermore the energy gap of HgTe at room temperature has also been determined. Magneto-transport measurements of n-type QWs show very pronounced Shubnikov-de Haas (SdH) oscillations and well developed quantum Hall plateaus for temperatures up to approximately 60 K. A large Rashba spin–orbit splitting of the first conduction subband, H1, has been observed in HgTe/Hg(1−x)Cd(x)Te QWs with an inverted band structure. Self-consistent Hartree calculations of the band structure based on the above model allows us to quantitatively describe the experimental results and demonstrates that the heavy hole nature of the H1 subband greatly influences the spatial distribution of electrons in the QW and thus enhances the Rashba spin splitting, i.e. ΔE_H1=βk∥^3. Furthermore, the presence of two periodic SdH oscillations in p-type QWs with an inverted band structure has been observed and is the first direct evidence that these heterostructures are indirect semiconductors. The influence of Mn in the upper barrier on the 2D electrons in the well has been investigated as a function of their separation. With spacer thicknesses of 10 and 15 nm, no appreciable change is observed, however, a reduction of the spacer thickness to 5 nm results in an increase in the maximum population difference between the two Rashba spin split H1 subbands by a factor of approximately two.

@article{becker2002growth, abstract = {The MBE growth of Hg(1−x)Cd(x)Te alloys and type III HgTe/Hg(1−x)Cd(x)Te heterostructures has been discussed, including similarities and differences between the (0 0 1) and (1 1 2)B orientations. Furthermore the MBE growth of HgTe based quantum wells (QWs) with the incorporation of Mn are additional topics. An investigation of the optical properties of type III superlattices with a normal band structure has lead to information about band structure of these heterostructures as well as information about the interface and the semimetallic QW. For example, by means of the full 8×8 Kane Hamiltonian in the envelope function approximation, it has been demonstrated that the energy separation between the H1–E1 and L1–E1 intersubband transition energies is primarily determined by the valence band offset, Λ, between HgTe and CdTe. This has led to unambiguous values for the offset and its temperature dependence, i.e. Λ(T)=570±60 meV and dΛ/dT=−0.40±0.04T meV/K. Furthermore the energy gap of HgTe at room temperature has also been determined. Magneto-transport measurements of n-type QWs show very pronounced Shubnikov-de Haas (SdH) oscillations and well developed quantum Hall plateaus for temperatures up to approximately 60 K. A large Rashba spin–orbit splitting of the first conduction subband, H1, has been observed in HgTe/Hg(1−x)Cd(x)Te QWs with an inverted band structure. Self-consistent Hartree calculations of the band structure based on the above model allows us to quantitatively describe the experimental results and demonstrates that the heavy hole nature of the H1 subband greatly influences the spatial distribution of electrons in the QW and thus enhances the Rashba spin splitting, i.e. ΔE_H1=βk∥^3. Furthermore, the presence of two periodic SdH oscillations in p-type QWs with an inverted band structure has been observed and is the first direct evidence that these heterostructures are indirect semiconductors. The influence of Mn in the upper barrier on the 2D electrons in the well has been investigated as a function of their separation. With spacer thicknesses of 10 and 15 nm, no appreciable change is observed, however, a reduction of the spacer thickness to 5 nm results in an increase in the maximum population difference between the two Rashba spin split H1 subbands by a factor of approximately two.}, author = {Becker, C.R and Zhang, X.C and Ortner, K and Schmidt, J and Pfeuffer-Jeschke, A and Latussek, V and Gui, Y.S and Daumer, V and Liu, J and Buhmann, H and Landwehr, G and Molenkamp, L.W}, journal = {Thin Solid Films}, keywords = {qt}, month = {06}, number = {1-2}, pages = {129–138}, publisher = {Elsevier {BV}}, title = {{MBE} growth and characterization of Hg based compounds and heterostructures}, volume = 412, year = 2002 }

%0 Journal Article %1 becker2002growth %A Becker, C.R %A Zhang, X.C %A Ortner, K %A Schmidt, J %A Pfeuffer-Jeschke, A %A Latussek, V %A Gui, Y.S %A Daumer, V %A Liu, J %A Buhmann, H %A Landwehr, G %A Molenkamp, L.W %D 2002 %I Elsevier {BV} %J Thin Solid Films %N 1-2 %P 129--138 %R 10.1016/s0040-6090(02)00324-3 %T {MBE} growth and characterization of Hg based compounds and heterostructures %V 412 %X The MBE growth of Hg(1−x)Cd(x)Te alloys and type III HgTe/Hg(1−x)Cd(x)Te heterostructures has been discussed, including similarities and differences between the (0 0 1) and (1 1 2)B orientations. Furthermore the MBE growth of HgTe based quantum wells (QWs) with the incorporation of Mn are additional topics. An investigation of the optical properties of type III superlattices with a normal band structure has lead to information about band structure of these heterostructures as well as information about the interface and the semimetallic QW. For example, by means of the full 8×8 Kane Hamiltonian in the envelope function approximation, it has been demonstrated that the energy separation between the H1–E1 and L1–E1 intersubband transition energies is primarily determined by the valence band offset, Λ, between HgTe and CdTe. This has led to unambiguous values for the offset and its temperature dependence, i.e. Λ(T)=570±60 meV and dΛ/dT=−0.40±0.04T meV/K. Furthermore the energy gap of HgTe at room temperature has also been determined. Magneto-transport measurements of n-type QWs show very pronounced Shubnikov-de Haas (SdH) oscillations and well developed quantum Hall plateaus for temperatures up to approximately 60 K. A large Rashba spin–orbit splitting of the first conduction subband, H1, has been observed in HgTe/Hg(1−x)Cd(x)Te QWs with an inverted band structure. Self-consistent Hartree calculations of the band structure based on the above model allows us to quantitatively describe the experimental results and demonstrates that the heavy hole nature of the H1 subband greatly influences the spatial distribution of electrons in the QW and thus enhances the Rashba spin splitting, i.e. ΔE_H1=βk∥^3. Furthermore, the presence of two periodic SdH oscillations in p-type QWs with an inverted band structure has been observed and is the first direct evidence that these heterostructures are indirect semiconductors. The influence of Mn in the upper barrier on the 2D electrons in the well has been investigated as a function of their separation. With spacer thicknesses of 10 and 15 nm, no appreciable change is observed, however, a reduction of the spacer thickness to 5 nm results in an increase in the maximum population difference between the two Rashba spin split H1 subbands by a factor of approximately two.
Large Rashba spin-orbit splitting in gate controlled n-type modulation doped HgTe/Hg(0.3)Cd(0.7-x)Mn(x)Te quantum wells. Gui, Y.S.; Liu, J.; Daumer, V.; Becker, C.R.; Buhmann, H.; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 12(1-4), pp. 416–419. Elsevier {BV}, 2002.
- [ Abstract ]
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A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.

@article{gui2002large, abstract = {A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.}, author = {Gui, Y.S. and Liu, J. and Daumer, V. and Becker, C.R. and Buhmann, H. and Molenkamp, L.W.}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {01}, number = {1-4}, pages = {416–419}, publisher = {Elsevier {BV}}, title = {Large Rashba spin-orbit splitting in gate controlled n-type modulation doped HgTe/Hg(0.3)Cd(0.7-x)Mn(x)Te quantum wells}, volume = 12, year = 2002 }

%0 Journal Article %1 gui2002large %A Gui, Y.S. %A Liu, J. %A Daumer, V. %A Becker, C.R. %A Buhmann, H. %A Molenkamp, L.W. %D 2002 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 416--419 %R 10.1016/s1386-9477(01)00320-4 %T Large Rashba spin-orbit splitting in gate controlled n-type modulation doped HgTe/Hg(0.3)Cd(0.7-x)Mn(x)Te quantum wells %V 12 %X A quantum-mechanical model based on a Green’s function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, backscattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield information about the distribution, size, and the energetic height of the scattering potentials.
Growth and Magneto-Transport of Gate Controlled n Type HgTe/Hg(0.3)Cd(0.7)Te Quantum Wells with Inclusion of Mn. Becker, C.R.; Gui, Y.S.; Liu, J.; Daumer, V.; Ortner, K.; Hock, V.; Pfeuffer-Jeschke, A.; Buhmann, H.; Molenkamp, L.W. In Physica Status Solidi B, 229(2), pp. 775–779. 2002.
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A series of gate controlled n-type asymmetrically modulation doped HgTe quantum wells (QWs) with Mn in one of the barriers have been investigated. From a Fourier analysis of the Shubnikov-de Haas (SdH) oscillations, the population difference of the two spin split H1 subbands has been determined for three QWs with different spacer thicknesses between the quantum well and the Mn ions. This population difference shows a significant enhancement in the QW with a 5 nm spacer compared to the QWs with 10 and 15 nm thick spacers. The latter results agree with the predictions for Rashba spin–orbit splitting, however, we must assume that Mn in the QW with the thin spacer increases the asymmetry of the QW.

@article{becker2001growth, abstract = {A series of gate controlled n-type asymmetrically modulation doped HgTe quantum wells (QWs) with Mn in one of the barriers have been investigated. From a Fourier analysis of the Shubnikov-de Haas (SdH) oscillations, the population difference of the two spin split H1 subbands has been determined for three QWs with different spacer thicknesses between the quantum well and the Mn ions. This population difference shows a significant enhancement in the QW with a 5 nm spacer compared to the QWs with 10 and 15 nm thick spacers. The latter results agree with the predictions for Rashba spin–orbit splitting, however, we must assume that Mn in the QW with the thin spacer increases the asymmetry of the QW.}, author = {Becker, C.R. and Gui, Y.S. and Liu, J. and Daumer, V. and Ortner, K. and Hock, V. and Pfeuffer-Jeschke, A. and Buhmann, H. and Molenkamp, L.W.}, journal = {Physica Status Solidi B}, keywords = {qt}, month = {01}, number = 2, pages = {775–779}, title = {Growth and Magneto-Transport of Gate Controlled n Type HgTe/Hg(0.3)Cd(0.7)Te Quantum Wells with Inclusion of Mn}, volume = 229, year = 2002 }

%0 Journal Article %1 becker2001growth %A Becker, C.R. %A Gui, Y.S. %A Liu, J. %A Daumer, V. %A Ortner, K. %A Hock, V. %A Pfeuffer-Jeschke, A. %A Buhmann, H. %A Molenkamp, L.W. %D 2002 %J Physica Status Solidi B %N 2 %P 775--779 %R 10.1002/1521-3951(200201)229:2<775::AID-PSSB775>3.0.CO;2-W %T Growth and Magneto-Transport of Gate Controlled n Type HgTe/Hg(0.3)Cd(0.7)Te Quantum Wells with Inclusion of Mn %V 229 %X A series of gate controlled n-type asymmetrically modulation doped HgTe quantum wells (QWs) with Mn in one of the barriers have been investigated. From a Fourier analysis of the Shubnikov-de Haas (SdH) oscillations, the population difference of the two spin split H1 subbands has been determined for three QWs with different spacer thicknesses between the quantum well and the Mn ions. This population difference shows a significant enhancement in the QW with a 5 nm spacer compared to the QWs with 10 and 15 nm thick spacers. The latter results agree with the predictions for Rashba spin–orbit splitting, however, we must assume that Mn in the QW with the thin spacer increases the asymmetry of the QW.
Electron-wave diffraction by density inhomogeneities in two-dimensional electron gas. Novik, E.G.; Buhmann, H.; Maximov, S.; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 12(1-4), pp. 237–240. Elsevier {BV}, 2002.
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A model for the simulation of the interference patterns of an electron beam in a 2DEG in the presence of a perpendicular magnetic field is presented. The model is based on the Green function method and includes a realistic description of the scattering potential leading to electron interference effects in the 2DEG. Detailed information about distribution, strength and the size of the scattering potential are obtained from the simulation of the experimentally observed interference patterns. The results confirm theoretical assumptions about density-fluctuation correlations in a 2DEG.

@article{novik2002electronwave, abstract = {A model for the simulation of the interference patterns of an electron beam in a 2DEG in the presence of a perpendicular magnetic field is presented. The model is based on the Green function method and includes a realistic description of the scattering potential leading to electron interference effects in the 2DEG. Detailed information about distribution, strength and the size of the scattering potential are obtained from the simulation of the experimentally observed interference patterns. The results confirm theoretical assumptions about density-fluctuation correlations in a 2DEG.}, author = {Novik, E.G. and Buhmann, H. and Maximov, S. and Molenkamp, L.W.}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {01}, number = {1-4}, pages = {237–240}, publisher = {Elsevier {BV}}, title = {Electron-wave diffraction by density inhomogeneities in two-dimensional electron gas}, volume = 12, year = 2002 }

%0 Journal Article %1 novik2002electronwave %A Novik, E.G. %A Buhmann, H. %A Maximov, S. %A Molenkamp, L.W. %D 2002 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 237--240 %R 10.1016/s1386-9477(01)00362-9 %T Electron-wave diffraction by density inhomogeneities in two-dimensional electron gas %V 12 %X A model for the simulation of the interference patterns of an electron beam in a 2DEG in the presence of a perpendicular magnetic field is presented. The model is based on the Green function method and includes a realistic description of the scattering potential leading to electron interference effects in the 2DEG. Detailed information about distribution, strength and the size of the scattering potential are obtained from the simulation of the experimentally observed interference patterns. The results confirm theoretical assumptions about density-fluctuation correlations in a 2DEG.
1D diffusion: a novel transport regime in narrow 2DEG channels. Buhmann, H.; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 12(1-4), pp. 715–718. Elsevier {BV}, 2002.
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The transport properties of a two-dimensional electron gas (2DEG) in a narrow electron channel were studied as a function of magnetic field and electron current. When the channel width is smaller than the electron mean free path the non-linear resistance as a function of electron current has been interpreted in terms of Knudsen and Poiseuille transport regimes, in analogy to the molecular flow of gas atoms in a tube. However, a positive magneto-resistance is observed in an electron temperature range beyond the Knudsen regime which contradicts expected Poiseuille transport characteristics. We can trace this unexpected behaviour to the nature of electron–electron scattering processes in a system of reduced dimensionality. The character of the transport in this new regime can be viewed as a one-dimensional (1d) diffusion caused by the interplay of the two most dominant electron scattering processes in a 2DEG.

@article{buhmann2002diffusion, abstract = {The transport properties of a two-dimensional electron gas (2DEG) in a narrow electron channel were studied as a function of magnetic field and electron current. When the channel width is smaller than the electron mean free path the non-linear resistance as a function of electron current has been interpreted in terms of Knudsen and Poiseuille transport regimes, in analogy to the molecular flow of gas atoms in a tube. However, a positive magneto-resistance is observed in an electron temperature range beyond the Knudsen regime which contradicts expected Poiseuille transport characteristics. We can trace this unexpected behaviour to the nature of electron–electron scattering processes in a system of reduced dimensionality. The character of the transport in this new regime can be viewed as a one-dimensional (1d) diffusion caused by the interplay of the two most dominant electron scattering processes in a 2DEG.}, author = {Buhmann, H. and Molenkamp, L.W.}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {01}, number = {1-4}, pages = {715–718}, publisher = {Elsevier {BV}}, title = {1D diffusion: a novel transport regime in narrow 2DEG channels}, volume = 12, year = 2002 }

%0 Journal Article %1 buhmann2002diffusion %A Buhmann, H. %A Molenkamp, L.W. %D 2002 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 715--718 %R 10.1016/s1386-9477(01)00387-3 %T 1D diffusion: a novel transport regime in narrow 2DEG channels %V 12 %X The transport properties of a two-dimensional electron gas (2DEG) in a narrow electron channel were studied as a function of magnetic field and electron current. When the channel width is smaller than the electron mean free path the non-linear resistance as a function of electron current has been interpreted in terms of Knudsen and Poiseuille transport regimes, in analogy to the molecular flow of gas atoms in a tube. However, a positive magneto-resistance is observed in an electron temperature range beyond the Knudsen regime which contradicts expected Poiseuille transport characteristics. We can trace this unexpected behaviour to the nature of electron–electron scattering processes in a system of reduced dimensionality. The character of the transport in this new regime can be viewed as a one-dimensional (1d) diffusion caused by the interplay of the two most dominant electron scattering processes in a 2DEG.

Rashba splitting in n-type modulation-doped HgTe quantum wells with an inverted band structure. Zhang, X. C.; Pfeuffer-Jeschke, A.; Ortner, K.; Hock, V.; Buhmann, H.; Becker, C. R.; Landwehr, G. In Phys. Rev. B, 63(24), p. 245305. American Physical Society, 2001.
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Rashba spin splitting has been observed in the first conduction subband of n-type modulation-doped HgTe quantum wells (QW’s) with an inverted band structure via an investigation of Shubnikov–de Haas oscillations in gated Hall bars. In accordance with calculations, no spin splitting was observed in the second conduction subband (E2), but an obvious Rashba splitting is present in the first heavy-hole-like conduction subband (H1) that displays a large dependence on gate voltage. Self-consistent Hartree calculations of the band structure based on an 8×8k⋅p model are compared with experiment, which enables us to understand and quantitatively describe the experimental results. It has been shown that the heavy-hole nature of the H1 conduction subband greatly influences the spatial distribution of electrons in the QW and also enhances the Rashba spin splitting at large electron densities. These are unique features of type III heterostructures in the inverted band regime. The βk^3∥ dispersion predicted by an analytical model is a good approximation of the self-consistent Hartree calculations for small values of the in-plane wave-vector k∥ and has consequently been employed to describe the spin splitting of the H1 conduction subband rather than the commonly used αk∥ dispersion for the conduction subband in type I heterojunctions. The relative magnitude of Rashba splitting in the H1 and E2 subbands as well as the splitting of the H1 subband for different well widths are also presented.

@article{zhang2001rashba, abstract = {Rashba spin splitting has been observed in the first conduction subband of n-type modulation-doped HgTe quantum wells (QW’s) with an inverted band structure via an investigation of Shubnikov–de Haas oscillations in gated Hall bars. In accordance with calculations, no spin splitting was observed in the second conduction subband (E2), but an obvious Rashba splitting is present in the first heavy-hole-like conduction subband (H1) that displays a large dependence on gate voltage. Self-consistent Hartree calculations of the band structure based on an 8×8k⋅p model are compared with experiment, which enables us to understand and quantitatively describe the experimental results. It has been shown that the heavy-hole nature of the H1 conduction subband greatly influences the spatial distribution of electrons in the QW and also enhances the Rashba spin splitting at large electron densities. These are unique features of type III heterostructures in the inverted band regime. The βk^3∥ dispersion predicted by an analytical model is a good approximation of the self-consistent Hartree calculations for small values of the in-plane wave-vector k∥ and has consequently been employed to describe the spin splitting of the H1 conduction subband rather than the commonly used αk∥ dispersion for the conduction subband in type I heterojunctions. The relative magnitude of Rashba splitting in the H1 and E2 subbands as well as the splitting of the H1 subband for different well widths are also presented.}, author = {Zhang, X. C. and Pfeuffer-Jeschke, A. and Ortner, K. and Hock, V. and Buhmann, H. and Becker, C. R. and Landwehr, G.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {05}, number = 24, pages = 245305, publisher = {American Physical Society}, title = {Rashba splitting in n-type modulation-doped HgTe quantum wells with an inverted band structure}, volume = 63, year = 2001 }

%0 Journal Article %1 zhang2001rashba %A Zhang, X. C. %A Pfeuffer-Jeschke, A. %A Ortner, K. %A Hock, V. %A Buhmann, H. %A Becker, C. R. %A Landwehr, G. %D 2001 %I American Physical Society %J Phys. Rev. B %N 24 %P 245305 %R 10.1103/PhysRevB.63.245305 %T Rashba splitting in n-type modulation-doped HgTe quantum wells with an inverted band structure %V 63 %X Rashba spin splitting has been observed in the first conduction subband of n-type modulation-doped HgTe quantum wells (QW’s) with an inverted band structure via an investigation of Shubnikov–de Haas oscillations in gated Hall bars. In accordance with calculations, no spin splitting was observed in the second conduction subband (E2), but an obvious Rashba splitting is present in the first heavy-hole-like conduction subband (H1) that displays a large dependence on gate voltage. Self-consistent Hartree calculations of the band structure based on an 8×8k⋅p model are compared with experiment, which enables us to understand and quantitatively describe the experimental results. It has been shown that the heavy-hole nature of the H1 conduction subband greatly influences the spatial distribution of electrons in the QW and also enhances the Rashba spin splitting at large electron densities. These are unique features of type III heterostructures in the inverted band regime. The βk^3∥ dispersion predicted by an analytical model is a good approximation of the self-consistent Hartree calculations for small values of the in-plane wave-vector k∥ and has consequently been employed to describe the spin splitting of the H1 conduction subband rather than the commonly used αk∥ dispersion for the conduction subband in type I heterojunctions. The relative magnitude of Rashba splitting in the H1 and E2 subbands as well as the splitting of the H1 subband for different well widths are also presented.
Antiferromagnetic temperature and effective spin in n-type Hg1−xMnxTe. Gui, Y. S.; Liu, J; Ortner, K; Daumer, V; Becker, C. R.; Buhmann, H; Molenkamp, L. W. In Appl. Phys. Lett., 79(9), pp. 1321–1323. American Institute of Physics, 2001.
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We have observed a characteristic modulation in the amplitude of the Shubnikov–de Haas (SdH) oscillations and a large shift of node position with increasing temperature in the semimagnetic semiconductor Hg(1−x)Mn(x)Te. The positions of the oscillation extrema are almost temperature independent, with the exception that their phase changes by π after passing the nodal point. These features can be explained in terms of the exchange interaction between conduction electrons and the localized spin moments of Mn ions. The antiferromagnetic temperature and effective spin have been deduced from the temperature-dependent node position in the SdH oscillations.

@article{gui2001antiferromagnetic, abstract = {We have observed a characteristic modulation in the amplitude of the Shubnikov–de Haas (SdH) oscillations and a large shift of node position with increasing temperature in the semimagnetic semiconductor Hg(1−x)Mn(x)Te. The positions of the oscillation extrema are almost temperature independent, with the exception that their phase changes by π after passing the nodal point. These features can be explained in terms of the exchange interaction between conduction electrons and the localized spin moments of Mn ions. The antiferromagnetic temperature and effective spin have been deduced from the temperature-dependent node position in the SdH oscillations.}, author = {Gui, Y. S. and Liu, J and Ortner, K and Daumer, V and Becker, C. R. and Buhmann, H and Molenkamp, L. W.}, booktitle = {Applied Physics Letters}, journal = {Appl. Phys. Lett.}, keywords = {qt}, month = {08}, number = 9, pages = {1321–1323}, publisher = {American Institute of Physics}, title = {Antiferromagnetic temperature and effective spin in n-type Hg1−xMnxTe}, volume = 79, year = 2001 }

%0 Journal Article %1 gui2001antiferromagnetic %A Gui, Y. S. %A Liu, J %A Ortner, K %A Daumer, V %A Becker, C. R. %A Buhmann, H %A Molenkamp, L. W. %B Applied Physics Letters %D 2001 %I American Institute of Physics %J Appl. Phys. Lett. %N 9 %P 1321--1323 %R 10.1063/1.1397275 %T Antiferromagnetic temperature and effective spin in n-type Hg1−xMnxTe %V 79 %X We have observed a characteristic modulation in the amplitude of the Shubnikov–de Haas (SdH) oscillations and a large shift of node position with increasing temperature in the semimagnetic semiconductor Hg(1−x)Mn(x)Te. The positions of the oscillation extrema are almost temperature independent, with the exception that their phase changes by π after passing the nodal point. These features can be explained in terms of the exchange interaction between conduction electrons and the localized spin moments of Mn ions. The antiferromagnetic temperature and effective spin have been deduced from the temperature-dependent node position in the SdH oscillations.
Angle-Resolved Spectroscopy of Electron-Electron Scattering in a 2D System. Yanovski, A.V.; Predel, H.; Buhmann, H.; Gurzhi, R.N.; Kopeliovich, A.I.; Kalinenko, A.N.; Molenkamp, L.W. In Europhysics Lett., 56(5), p. 709. 2001.
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Electron-beam propagation experiments have been used to determine the energy and angle dependence of electron-electron (ee) scattering in a two-dimensional electron gas (2DEG) in a very direct manner. The experimental results provide direct evidence for novel ee-scattering effects in 2D degenerate conductors. Most striking is the increased importance of small-angle scattering in a 2D system with decreasing excitation energy. In particular, in a 2DEG ee-scattering can, at sufficiently low energies, be purely dephasing in character, i.e. changing the phase but not the direction of electron motion.

@article{yanovski2001angleresolved, abstract = {Electron-beam propagation experiments have been used to determine the energy and angle dependence of electron-electron (ee) scattering in a two-dimensional electron gas (2DEG) in a very direct manner. The experimental results provide direct evidence for novel ee-scattering effects in 2D degenerate conductors. Most striking is the increased importance of small-angle scattering in a 2D system with decreasing excitation energy. In particular, in a 2DEG ee-scattering can, at sufficiently low energies, be purely dephasing in character, i.e. changing the phase but not the direction of electron motion.}, author = {Yanovski, A.V. and Predel, H. and Buhmann, H. and Gurzhi, R.N. and Kopeliovich, A.I. and Kalinenko, A.N. and Molenkamp, L.W.}, journal = {Europhysics Lett.}, keywords = {qt}, month = {09}, number = 5, pages = 709, title = {Angle-Resolved Spectroscopy of Electron-Electron Scattering in a 2D System}, volume = 56, year = 2001 }

%0 Journal Article %1 yanovski2001angleresolved %A Yanovski, A.V. %A Predel, H. %A Buhmann, H. %A Gurzhi, R.N. %A Kopeliovich, A.I. %A Kalinenko, A.N. %A Molenkamp, L.W. %D 2001 %J Europhysics Lett. %N 5 %P 709 %R 10.1209/epl/i2001-00578-y %T Angle-Resolved Spectroscopy of Electron-Electron Scattering in a 2D System %V 56 %X Electron-beam propagation experiments have been used to determine the energy and angle dependence of electron-electron (ee) scattering in a two-dimensional electron gas (2DEG) in a very direct manner. The experimental results provide direct evidence for novel ee-scattering effects in 2D degenerate conductors. Most striking is the increased importance of small-angle scattering in a 2D system with decreasing excitation energy. In particular, in a 2DEG ee-scattering can, at sufficiently low energies, be purely dephasing in character, i.e. changing the phase but not the direction of electron motion.

Thermopower of the molecular state in a double quantum dot. Chen, Xiaoshuang; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. B, 61(24), pp. 16801–16806. American Physical Society, 2000.
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The thermopower of the molecular state in a double quantum dot is studied using a mixed model, which combines the classical capacitance model and a valence-electron approach. Our calculations show that close to the triple points where the resonances of the two dots intersect, there are additional steplike structures in the thermopower that result from coupling of the “topmost” electronic states. Far away from the triple points, we find that, with increasing detuning, the steplike structures shift toward the center of two neighboring Coulomb blockade oscillations, while very far away from the triple points, the transport resembles that of a single dot of lower electrostatic energy. Our results are in qualitative agreement with experimental findings on the conductance of Blick et al. [Phys. Rev. Lett. 80, 4032 (1998)].

@article{chen2000thermopower, abstract = {The thermopower of the molecular state in a double quantum dot is studied using a mixed model, which combines the classical capacitance model and a valence-electron approach. Our calculations show that close to the triple points where the resonances of the two dots intersect, there are additional steplike structures in the thermopower that result from coupling of the “topmost” electronic states. Far away from the triple points, we find that, with increasing detuning, the steplike structures shift toward the center of two neighboring Coulomb blockade oscillations, while very far away from the triple points, the transport resembles that of a single dot of lower electrostatic energy. Our results are in qualitative agreement with experimental findings on the conductance of Blick et al. [Phys. Rev. Lett. 80, 4032 (1998)].}, author = {Chen, Xiaoshuang and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {06}, number = 24, pages = {16801–16806}, publisher = {American Physical Society}, title = {Thermopower of the molecular state in a double quantum dot}, volume = 61, year = 2000 }

%0 Journal Article %1 chen2000thermopower %A Chen, Xiaoshuang %A Buhmann, H. %A Molenkamp, L. W. %D 2000 %I American Physical Society %J Phys. Rev. B %N 24 %P 16801--16806 %R 10.1103/PhysRevB.61.16801 %T Thermopower of the molecular state in a double quantum dot %V 61 %X The thermopower of the molecular state in a double quantum dot is studied using a mixed model, which combines the classical capacitance model and a valence-electron approach. Our calculations show that close to the triple points where the resonances of the two dots intersect, there are additional steplike structures in the thermopower that result from coupling of the “topmost” electronic states. Far away from the triple points, we find that, with increasing detuning, the steplike structures shift toward the center of two neighboring Coulomb blockade oscillations, while very far away from the triple points, the transport resembles that of a single dot of lower electrostatic energy. Our results are in qualitative agreement with experimental findings on the conductance of Blick et al. [Phys. Rev. Lett. 80, 4032 (1998)].
Thermopower of quantum chaos. Buhmann, H; Molenkamp, L.W. In Physica E: Low-dimensional Systems and Nanostructures, 6(1-4), pp. 400–403. Elsevier {BV}, 2000.
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The thermopower of a chaotic quantum dot has been studied in the Coulomb and the ballistic transport regime. Theoretical examinations predict distinct features for quantum dots where the electron trajectories are chaotic. Accordingly, we give experimental evidence for a residual effective charging energy in the case of asymmetric ajusted leads (G⩽2e^2/h) and for non-Gaussian thermopower fluctuation distributions in the ballistic regime (G=4e^2/h).

@article{buhmann2000thermopower, abstract = {The thermopower of a chaotic quantum dot has been studied in the Coulomb and the ballistic transport regime. Theoretical examinations predict distinct features for quantum dots where the electron trajectories are chaotic. Accordingly, we give experimental evidence for a residual effective charging energy in the case of asymmetric ajusted leads (G⩽2e^2/h) and for non-Gaussian thermopower fluctuation distributions in the ballistic regime (G=4e^2/h).}, author = {Buhmann, H and Molenkamp, L.W}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {02}, number = {1-4}, pages = {400–403}, publisher = {Elsevier {BV}}, title = {Thermopower of quantum chaos}, volume = 6, year = 2000 }

%0 Journal Article %1 buhmann2000thermopower %A Buhmann, H %A Molenkamp, L.W %D 2000 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 400--403 %R 10.1016/s1386-9477(99)00207-6 %T Thermopower of quantum chaos %V 6 %X The thermopower of a chaotic quantum dot has been studied in the Coulomb and the ballistic transport regime. Theoretical examinations predict distinct features for quantum dots where the electron trajectories are chaotic. Accordingly, we give experimental evidence for a residual effective charging energy in the case of asymmetric ajusted leads (G⩽2e^2/h) and for non-Gaussian thermopower fluctuation distributions in the ballistic regime (G=4e^2/h).
Probing the Potential Landscape Inside a Two-Dimensional Electron Gas. Koonen, J. J.; Buhmann, H.; Molenkamp, L. W. In Phys. Rev. Lett., 84(11), pp. 2473–2476. American Physical Society, 2000.
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We report direct observations of the scattering potentials in a two-dimensional electron gas using electron-beam diffraction experiments. The diffracting objects are local density fluctuations caused by spatial and charge-state distribution of donors in the GaAs-(Al,Ga)As heterostructures. The scatterers can be manipulated externally by sample illumination or by cooling the sample down under depleted conditions.

@article{koonen2000probing, abstract = {We report direct observations of the scattering potentials in a two-dimensional electron gas using electron-beam diffraction experiments. The diffracting objects are local density fluctuations caused by spatial and charge-state distribution of donors in the GaAs-(Al,Ga)As heterostructures. The scatterers can be manipulated externally by sample illumination or by cooling the sample down under depleted conditions.}, author = {Koonen, J. J. and Buhmann, H. and Molenkamp, L. W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {03}, number = 11, pages = {2473–2476}, publisher = {American Physical Society}, title = {Probing the Potential Landscape Inside a Two-Dimensional Electron Gas}, volume = 84, year = 2000 }

%0 Journal Article %1 koonen2000probing %A Koonen, J. J. %A Buhmann, H. %A Molenkamp, L. W. %D 2000 %I American Physical Society %J Phys. Rev. Lett. %N 11 %P 2473--2476 %R 10.1103/PhysRevLett.84.2473 %T Probing the Potential Landscape Inside a Two-Dimensional Electron Gas %V 84 %X We report direct observations of the scattering potentials in a two-dimensional electron gas using electron-beam diffraction experiments. The diffracting objects are local density fluctuations caused by spatial and charge-state distribution of donors in the GaAs-(Al,Ga)As heterostructures. The scatterers can be manipulated externally by sample illumination or by cooling the sample down under depleted conditions.
New transport effects in a degenerate two-dimensional electron gas. Buhmann, H.; Gurzhi, R.N.; Kalinenko, A.N.; Kopeliovich, A.I.; Molenkamp, L.W.; Predel, H.; Yanovsky, A.V. In Physica B: Condensed Matter, 284-288, pp. 1904–1905. Elsevier {BV}, 2000.
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The influence of electron–electron (e–e) scattering on the transport properties of a two-dimensional electron-gas in (Al ,Ga)As-GaAs heterostructures is studied experimentally and theoretically. The important role of e–e collisions has been demonstrated. Due to phase space restrains small-angle scattering events are expected to dominate the propagation of non-equilibrium electrons. The experimental evidence is given via injection-energy-dependent electron beam experiments.

@article{buhmann2000transport, abstract = {The influence of electron–electron (e–e) scattering on the transport properties of a two-dimensional electron-gas in (Al ,Ga)As-GaAs heterostructures is studied experimentally and theoretically. The important role of e–e collisions has been demonstrated. Due to phase space restrains small-angle scattering events are expected to dominate the propagation of non-equilibrium electrons. The experimental evidence is given via injection-energy-dependent electron beam experiments.}, author = {Buhmann, H. and Gurzhi, R.N. and Kalinenko, A.N. and Kopeliovich, A.I. and Molenkamp, L.W. and Predel, H. and Yanovsky, A.V.}, journal = {Physica B: Condensed Matter}, keywords = {qt}, month = {07}, pages = {1904–1905}, publisher = {Elsevier {BV}}, title = {New transport effects in a degenerate two-dimensional electron gas}, volume = {284-288}, year = 2000 }

%0 Journal Article %1 buhmann2000transport %A Buhmann, H. %A Gurzhi, R.N. %A Kalinenko, A.N. %A Kopeliovich, A.I. %A Molenkamp, L.W. %A Predel, H. %A Yanovsky, A.V. %D 2000 %I Elsevier {BV} %J Physica B: Condensed Matter %P 1904--1905 %R 10.1016/s0921-4526(99)02996-8 %T New transport effects in a degenerate two-dimensional electron gas %V 284-288 %X The influence of electron–electron (e–e) scattering on the transport properties of a two-dimensional electron-gas in (Al ,Ga)As-GaAs heterostructures is studied experimentally and theoretically. The important role of e–e collisions has been demonstrated. Due to phase space restrains small-angle scattering events are expected to dominate the propagation of non-equilibrium electrons. The experimental evidence is given via injection-energy-dependent electron beam experiments.
Electron{\textendash}electron scattering and the propagation of electron beams in a two-dimensional electron gas. Buhmann, H; Predel, H; Molenkamp, L.W; Gurzhi, R.N; Kopeliovich, A.I; Kalinenko, A.N; Yanovsky, A.V. In Physica E: Low-dimensional Systems and Nanostructures, 6(1-4), pp. 310–313. Elsevier {BV}, 2000.
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Experimental studies of electron-beam propagation in a degenerate 2DEG in a GaAs-(Al,Ga)As heterostructure are presented for a wide range of injection energies, 0<E⩽E_F. The electron beam is injected and detected in the 2DEG via electrostatically defined quantum point-contacts with typical distances of . Energy-dependent beam injection is used to reveal the characteristics of the electron-beam propagation. Considering the specific character for electron–electron scattering events in 2D systems linearized Boltzmann equations could be used to model the experimental observations.

@article{buhmann2000electrontextendashelectron, abstract = {Experimental studies of electron-beam propagation in a degenerate 2DEG in a GaAs-(Al,Ga)As heterostructure are presented for a wide range of injection energies, 0<E⩽E_F. The electron beam is injected and detected in the 2DEG via electrostatically defined quantum point-contacts with typical distances of . Energy-dependent beam injection is used to reveal the characteristics of the electron-beam propagation. Considering the specific character for electron–electron scattering events in 2D systems linearized Boltzmann equations could be used to model the experimental observations.}, author = {Buhmann, H and Predel, H and Molenkamp, L.W and Gurzhi, R.N and Kopeliovich, A.I and Kalinenko, A.N and Yanovsky, A.V}, journal = {Physica E: Low-dimensional Systems and Nanostructures}, keywords = {qt}, month = {02}, number = {1-4}, pages = {310–313}, publisher = {Elsevier {BV}}, title = {Electron{\textendash}electron scattering and the propagation of electron beams in a two-dimensional electron gas}, volume = 6, year = 2000 }

%0 Journal Article %1 buhmann2000electrontextendashelectron %A Buhmann, H %A Predel, H %A Molenkamp, L.W %A Gurzhi, R.N %A Kopeliovich, A.I %A Kalinenko, A.N %A Yanovsky, A.V %D 2000 %I Elsevier {BV} %J Physica E: Low-dimensional Systems and Nanostructures %N 1-4 %P 310--313 %R 10.1016/s1386-9477(99)00163-0 %T Electron{\textendash}electron scattering and the propagation of electron beams in a two-dimensional electron gas %V 6 %X Experimental studies of electron-beam propagation in a degenerate 2DEG in a GaAs-(Al,Ga)As heterostructure are presented for a wide range of injection energies, 0<E⩽E_F. The electron beam is injected and detected in the 2DEG via electrostatically defined quantum point-contacts with typical distances of . Energy-dependent beam injection is used to reveal the characteristics of the electron-beam propagation. Considering the specific character for electron–electron scattering events in 2D systems linearized Boltzmann equations could be used to model the experimental observations.
Effects of electron-electron scattering on electron-beam propagation in a two-dimensional electron gas. Predel, H.; Buhmann, H.; Molenkamp, L. W.; Gurzhi, R. N.; Kalinenko, A. N.; Kopeliovich, A. I.; Yanovsky, A. V. In Phys. Rev. B, 62(3), pp. 2057–2064. American Physical Society, 2000.
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We have studied experimentally and theoretically the influence of electron-electron collisions on the propagation of electron beams in a two-dimensional electron gas for excess injection energies ranging from zero up to the Fermi energy. We find that the detector signal consists of quasiballistic electrons, which either have not undergone any electron-electron collisions or have only been scattered at small angles. Theoretically, the small-angle scattering exhibits distinct features that can be traced back to the reduced dimensionality of the electron system. A number of nonlinear effects, also related to the two-dimensional character of the system, are discussed. In the simplest situation, the heating of the electron gas by the high-energy part of the beam leads to a weakening of the signal of quasiballistic electrons and to the appearance of thermovoltage. This results in a nonmonotonic dependence of the detector signal on the intensity of the injected beam, as observed experimentally.

@article{predel2000effects, abstract = {We have studied experimentally and theoretically the influence of electron-electron collisions on the propagation of electron beams in a two-dimensional electron gas for excess injection energies ranging from zero up to the Fermi energy. We find that the detector signal consists of quasiballistic electrons, which either have not undergone any electron-electron collisions or have only been scattered at small angles. Theoretically, the small-angle scattering exhibits distinct features that can be traced back to the reduced dimensionality of the electron system. A number of nonlinear effects, also related to the two-dimensional character of the system, are discussed. In the simplest situation, the heating of the electron gas by the high-energy part of the beam leads to a weakening of the signal of quasiballistic electrons and to the appearance of thermovoltage. This results in a nonmonotonic dependence of the detector signal on the intensity of the injected beam, as observed experimentally.}, author = {Predel, H. and Buhmann, H. and Molenkamp, L. W. and Gurzhi, R. N. and Kalinenko, A. N. and Kopeliovich, A. I. and Yanovsky, A. V.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {07}, number = 3, pages = {2057–2064}, publisher = {American Physical Society}, title = {Effects of electron-electron scattering on electron-beam propagation in a two-dimensional electron gas}, volume = 62, year = 2000 }

%0 Journal Article %1 predel2000effects %A Predel, H. %A Buhmann, H. %A Molenkamp, L. W. %A Gurzhi, R. N. %A Kalinenko, A. N. %A Kopeliovich, A. I. %A Yanovsky, A. V. %D 2000 %I American Physical Society %J Phys. Rev. B %N 3 %P 2057--2064 %R 10.1103/PhysRevB.62.2057 %T Effects of electron-electron scattering on electron-beam propagation in a two-dimensional electron gas %V 62 %X We have studied experimentally and theoretically the influence of electron-electron collisions on the propagation of electron beams in a two-dimensional electron gas for excess injection energies ranging from zero up to the Fermi energy. We find that the detector signal consists of quasiballistic electrons, which either have not undergone any electron-electron collisions or have only been scattered at small angles. Theoretically, the small-angle scattering exhibits distinct features that can be traced back to the reduced dimensionality of the electron system. A number of nonlinear effects, also related to the two-dimensional character of the system, are discussed. In the simplest situation, the heating of the electron gas by the high-energy part of the beam leads to a weakening of the signal of quasiballistic electrons and to the appearance of thermovoltage. This results in a nonmonotonic dependence of the detector signal on the intensity of the injected beam, as observed experimentally.

Thermopower of a Chaotic Quantum Dot. Godijn, S. F.; Möller, S.; Buhmann, H.; Molenkamp, L. W.; van Langen, S. A. In Phys. Rev. Lett., 82(14), pp. 2927–2930. American Physical Society, 1999.
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The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using random matrix theory. We observe no contributions from weak localization or short trajectories in the thermopower.

@article{godijn1999thermopower, abstract = {The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using random matrix theory. We observe no contributions from weak localization or short trajectories in the thermopower.}, author = {Godijn, S. F. and M\"oller, S. and Buhmann, H. and Molenkamp, L. W. and van Langen, S. A.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = {04}, number = 14, pages = {2927–2930}, publisher = {American Physical Society}, title = {Thermopower of a Chaotic Quantum Dot}, volume = 82, year = 1999 }

%0 Journal Article %1 godijn1999thermopower %A Godijn, S. F. %A Möller, S. %A Buhmann, H. %A Molenkamp, L. W. %A van Langen, S. A. %D 1999 %I American Physical Society %J Phys. Rev. Lett. %N 14 %P 2927--2930 %R 10.1103/PhysRevLett.82.2927 %T Thermopower of a Chaotic Quantum Dot %V 82 %X The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using random matrix theory. We observe no contributions from weak localization or short trajectories in the thermopower.
On electron-electron scattering mechanisms in 2D degenerated systems. Buhmann, H.; Gurzhi, R.N.; Kalinenko, A.N.; Kopeliovich, A.I.; Molenkamp, L.W.; Yanovsky, A.V. In Nanostructured Materials, 12(5-8), pp. 835–838. Elsevier {BV}, 1999.
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The detailed quantitative theory of electron-electron scattering processes in 2D electron degenerated systems in GaAs(AlGaAs) heterostructures has been developed on the basis of analytical treatment and numerical calculations. We have found the conditions and intervals of values of the characteristic parameters in which specific properties of 2D relaxation predicted previously on the theoretical level manifest themselves. New effects, i.e. a secondary beam of electrons scattered back and a very narrow beam of holes moving in the direction of injection, have been found.

@article{buhmann1999electronelectron, abstract = {The detailed quantitative theory of electron-electron scattering processes in 2D electron degenerated systems in GaAs(AlGaAs) heterostructures has been developed on the basis of analytical treatment and numerical calculations. We have found the conditions and intervals of values of the characteristic parameters in which specific properties of 2D relaxation predicted previously on the theoretical level manifest themselves. New effects, i.e. a secondary beam of electrons scattered back and a very narrow beam of holes moving in the direction of injection, have been found.}, author = {Buhmann, H. and Gurzhi, R.N. and Kalinenko, A.N. and Kopeliovich, A.I. and Molenkamp, L.W. and Yanovsky, A.V.}, journal = {Nanostructured Materials}, keywords = {qt}, month = {01}, number = {5-8}, pages = {835–838}, publisher = {Elsevier {BV}}, title = {On electron-electron scattering mechanisms in 2D degenerated systems}, volume = 12, year = 1999 }

%0 Journal Article %1 buhmann1999electronelectron %A Buhmann, H. %A Gurzhi, R.N. %A Kalinenko, A.N. %A Kopeliovich, A.I. %A Molenkamp, L.W. %A Yanovsky, A.V. %D 1999 %I Elsevier {BV} %J Nanostructured Materials %N 5-8 %P 835--838 %R 10.1016/s0965-9773(99)00246-9 %T On electron-electron scattering mechanisms in 2D degenerated systems %V 12 %X The detailed quantitative theory of electron-electron scattering processes in 2D electron degenerated systems in GaAs(AlGaAs) heterostructures has been developed on the basis of analytical treatment and numerical calculations. We have found the conditions and intervals of values of the characteristic parameters in which specific properties of 2D relaxation predicted previously on the theoretical level manifest themselves. New effects, i.e. a secondary beam of electrons scattered back and a very narrow beam of holes moving in the direction of injection, have been found.
Charge fluctuations, chaotic trajectories, and the coulomb blockade. Buhmann, H.; Möller, S.; Molenkamp, L.W. In Festkörperprobleme / Advances in Solid State Physics, Vol. 38, B. Kramer (ed.), pp. 193–202. 1999.
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Two different experimental methods have been used to determine the charging energy U* of a quantum dot as a function of the coupling to the external leads. A powerlaw scaling behaviour depending on the number of opening leads was observed for the weak coupling regime in both types of experiments, in agreement with theories based on the Tomonaga-Luttinger formalism. For stronger coupling (t > 0.5), in asymetric quantum dots with only one opening lead, U* appears to reach a constant value. This latter behaviour can be explained by taking into account chaotic motion of the electrons in quantum dots.

@inbook{buhmann1999charge, abstract = {Two different experimental methods have been used to determine the charging energy U* of a quantum dot as a function of the coupling to the external leads. A powerlaw scaling behaviour depending on the number of opening leads was observed for the weak coupling regime in both types of experiments, in agreement with theories based on the Tomonaga-Luttinger formalism. For stronger coupling (t > 0.5), in asymetric quantum dots with only one opening lead, U* appears to reach a constant value. This latter behaviour can be explained by taking into account chaotic motion of the electrons in quantum dots.}, author = {Buhmann, H. and Möller, S. and Molenkamp, L.W.}, booktitle = {Festkörperprobleme / Advances in Solid State Physics}, editor = {Kramer, B.}, keywords = {qt}, pages = {193–202}, title = {Charge fluctuations, chaotic trajectories, and the coulomb blockade}, volume = 38, year = 1999 }

%0 Book Section %1 buhmann1999charge %A Buhmann, H. %A Möller, S. %A Molenkamp, L.W. %B Festkörperprobleme / Advances in Solid State Physics %D 1999 %E Kramer, B. %P 193--202 %T Charge fluctuations, chaotic trajectories, and the coulomb blockade %U http://www.springer.com/la/book/9783662161272 %V 38 %X Two different experimental methods have been used to determine the charging energy U* of a quantum dot as a function of the coupling to the external leads. A powerlaw scaling behaviour depending on the number of opening leads was observed for the weak coupling regime in both types of experiments, in agreement with theories based on the Tomonaga-Luttinger formalism. For stronger coupling (t > 0.5), in asymetric quantum dots with only one opening lead, U* appears to reach a constant value. This latter behaviour can be explained by taking into account chaotic motion of the electrons in quantum dots.

On dynamic properties of a two-dimensional degenerate electron gas. Buhmann, H; Molenkamp, L. W.; Gurzhi, R. N.; Kalinenko, A. N.; Kopeliovich, A. I.; Yanovsky, A. V. In Low Temperature Physics, 24(10), pp. 737–741. American Institute of Physics, 1998.
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A detailed theory of electron–electron scattering in two-dimensional degenerate systems in heterostructures is constructed as a result of analysis and numerical computations. The conditions are formulated and the values of characteristic parameters are obtained for which specific two-dimensional effects predicted earlier from theoretical considerations can be observed. New properties of scattering indicatrix, viz., a beam of electrons flying almost antiparallel to the primary beam and a very narrow beam of holes flying in the forward direction, are found.

@article{buhmann1998dynamic, abstract = {A detailed theory of electron–electron scattering in two-dimensional degenerate systems in heterostructures is constructed as a result of analysis and numerical computations. The conditions are formulated and the values of characteristic parameters are obtained for which specific two-dimensional effects predicted earlier from theoretical considerations can be observed. New properties of scattering indicatrix, viz., a beam of electrons flying almost antiparallel to the primary beam and a very narrow beam of holes flying in the forward direction, are found.}, author = {Buhmann, H and Molenkamp, L. W. and Gurzhi, R. N. and Kalinenko, A. N. and Kopeliovich, A. I. and Yanovsky, A. V.}, booktitle = {Low Temperature Physics}, journal = {Low Temperature Physics}, keywords = {qt}, month = 10, number = 10, pages = {737–741}, publisher = {American Institute of Physics}, title = {On dynamic properties of a two-dimensional degenerate electron gas}, volume = 24, year = 1998 }

%0 Journal Article %1 buhmann1998dynamic %A Buhmann, H %A Molenkamp, L. W. %A Gurzhi, R. N. %A Kalinenko, A. N. %A Kopeliovich, A. I. %A Yanovsky, A. V. %B Low Temperature Physics %D 1998 %I American Institute of Physics %J Low Temperature Physics %N 10 %P 737--741 %R 10.1063/1.593663 %T On dynamic properties of a two-dimensional degenerate electron gas %V 24 %X A detailed theory of electron–electron scattering in two-dimensional degenerate systems in heterostructures is constructed as a result of analysis and numerical computations. The conditions are formulated and the values of characteristic parameters are obtained for which specific two-dimensional effects predicted earlier from theoretical considerations can be observed. New properties of scattering indicatrix, viz., a beam of electrons flying almost antiparallel to the primary beam and a very narrow beam of holes flying in the forward direction, are found.
Magneto-thermopower of a chaotic, ballistic quantum dot. Buhmann, H.; Möller, S.; Godijn, S.F.; Molenkamp, L.W. In Physica B: Condensed Matter, 256-258, pp. 198–202. Elsevier {BV}, 1998.
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We present measurements of the magneto-thermopower fluctuations of a gate-defined, chaotic quantum dot in a (Al,Ga)As-semiconductor heterostructure. Current-heating techniques were employed to build up the necessary temperature difference across the quantum dot for the thermopower measurement. A statistical ensemble is generated by registering the magnetic-field and gate-voltage dependence for a number of slightly different dot sizes. The experimental results are in good agreement with the predicted non-gaussian distribution of the Random Matrix Theory. To our knowledge these are the first transport experiments that directly yield the non-gaussian distribution which are an unambiguous sign for the occurence of chaos.

@article{buhmann1998magnetothermopower, abstract = {We present measurements of the magneto-thermopower fluctuations of a gate-defined, chaotic quantum dot in a (Al,Ga)As-semiconductor heterostructure. Current-heating techniques were employed to build up the necessary temperature difference across the quantum dot for the thermopower measurement. A statistical ensemble is generated by registering the magnetic-field and gate-voltage dependence for a number of slightly different dot sizes. The experimental results are in good agreement with the predicted non-gaussian distribution of the Random Matrix Theory. To our knowledge these are the first transport experiments that directly yield the non-gaussian distribution which are an unambiguous sign for the occurence of chaos.}, author = {Buhmann, H. and Möller, S. and Godijn, S.F. and Molenkamp, L.W.}, journal = {Physica B: Condensed Matter}, keywords = {qt}, month = 12, pages = {198–202}, publisher = {Elsevier {BV}}, title = {Magneto-thermopower of a chaotic, ballistic quantum dot}, volume = {256-258}, year = 1998 }

%0 Journal Article %1 buhmann1998magnetothermopower %A Buhmann, H. %A Möller, S. %A Godijn, S.F. %A Molenkamp, L.W. %D 1998 %I Elsevier {BV} %J Physica B: Condensed Matter %P 198--202 %R 10.1016/s0921-4526(98)00515-8 %T Magneto-thermopower of a chaotic, ballistic quantum dot %V 256-258 %X We present measurements of the magneto-thermopower fluctuations of a gate-defined, chaotic quantum dot in a (Al,Ga)As-semiconductor heterostructure. Current-heating techniques were employed to build up the necessary temperature difference across the quantum dot for the thermopower measurement. A statistical ensemble is generated by registering the magnetic-field and gate-voltage dependence for a number of slightly different dot sizes. The experimental results are in good agreement with the predicted non-gaussian distribution of the Random Matrix Theory. To our knowledge these are the first transport experiments that directly yield the non-gaussian distribution which are an unambiguous sign for the occurence of chaos.
Classical rebound trajectories in nonlocal ballistic electron transport. Heindrichs, A. S. D.; Buhmann, H.; Godijn, S. F.; Molenkamp, L. W. In Phys. Rev. B, 57(7), pp. 3961–3965. American Physical Society, 1998.
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We demonstrate experimentally and by Monte Carlo simulation that the negative dips which occur at low magnetic fields on both sides of the main signal in nonlocal electron-beam measurements in semiconductor nanostructures result from electrons following classical rebound trajectories. We propose an alternative measurement geometry that eliminates these effects.

@article{PhysRevB.57.3961, abstract = {We demonstrate experimentally and by Monte Carlo simulation that the negative dips which occur at low magnetic fields on both sides of the main signal in nonlocal electron-beam measurements in semiconductor nanostructures result from electrons following classical rebound trajectories. We propose an alternative measurement geometry that eliminates these effects.}, author = {Heindrichs, A. S. D. and Buhmann, H. and Godijn, S. F. and Molenkamp, L. W.}, journal = {Phys. Rev. B}, keywords = {qt}, month = {02}, number = 7, pages = {3961–3965}, publisher = {American Physical Society}, title = {Classical rebound trajectories in nonlocal ballistic electron transport}, volume = 57, year = 1998 }

%0 Journal Article %1 PhysRevB.57.3961 %A Heindrichs, A. S. D. %A Buhmann, H. %A Godijn, S. F. %A Molenkamp, L. W. %D 1998 %I American Physical Society %J Phys. Rev. B %N 7 %P 3961--3965 %R 10.1103/PhysRevB.57.3961 %T Classical rebound trajectories in nonlocal ballistic electron transport %V 57 %X We demonstrate experimentally and by Monte Carlo simulation that the negative dips which occur at low magnetic fields on both sides of the main signal in nonlocal electron-beam measurements in semiconductor nanostructures result from electrons following classical rebound trajectories. We propose an alternative measurement geometry that eliminates these effects.
Charging Energy of a Chaotic Quantum Dot. Möller, S.; Buhmann, H.; Godijn, S. F.; Molenkamp, L. W. In Phys. Rev. Lett., 81(23), pp. 5197–5200. American Physical Society, 1998.
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The scaling behavior of the charging energy of a quantum dot with asymmetrically adjusted tunnel barriers is measured through the amplitude of the Coulomb oscillations in the thermovoltage. For weak coupling between the dot and the reservoirs, we observe a linear scaling of the effective charging energy when the transmission probability of one tunnel barrier is increased. At higher transmission probabilities, we find a deviation from the linear scaling and a crossover to a constant value. This behavior is caused by the chaotic nature of the electron trajectories within the dot.

@article{moller1998charging, abstract = {The scaling behavior of the charging energy of a quantum dot with asymmetrically adjusted tunnel barriers is measured through the amplitude of the Coulomb oscillations in the thermovoltage. For weak coupling between the dot and the reservoirs, we observe a linear scaling of the effective charging energy when the transmission probability of one tunnel barrier is increased. At higher transmission probabilities, we find a deviation from the linear scaling and a crossover to a constant value. This behavior is caused by the chaotic nature of the electron trajectories within the dot.}, author = {M\"oller, S. and Buhmann, H. and Godijn, S. F. and Molenkamp, L. W.}, journal = {Phys. Rev. Lett.}, keywords = {qt}, month = 12, number = 23, pages = {5197–5200}, publisher = {American Physical Society}, title = {Charging Energy of a Chaotic Quantum Dot}, volume = 81, year = 1998 }

%0 Journal Article %1 moller1998charging %A Möller, S. %A Buhmann, H. %A Godijn, S. F. %A Molenkamp, L. W. %D 1998 %I American Physical Society %J Phys. Rev. Lett. %N 23 %P 5197--5200 %R 10.1103/PhysRevLett.81.5197 %T Charging Energy of a Chaotic Quantum Dot %V 81 %X The scaling behavior of the charging energy of a quantum dot with asymmetrically adjusted tunnel barriers is measured through the amplitude of the Coulomb oscillations in the thermovoltage. For weak coupling between the dot and the reservoirs, we observe a linear scaling of the effective charging energy when the transmission probability of one tunnel barrier is increased. At higher transmission probabilities, we find a deviation from the linear scaling and a crossover to a constant value. This behavior is caused by the chaotic nature of the electron trajectories within the dot.

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