
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) (2015). 213(3) 582590.
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) (2015). 213(3) 626634.
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 (2015). 17 113003.
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 MagnetoPhotoresponse of a HgTeBased TwoDimensional Electron Gas. Pakmehr, M.; Brüne, C.; Buhmann, H.; Molenkamp, L. W.; McCombe, B. D. in Selected Topics in Electronics and Systems (2015). 56 6773.
HgTe quantum wells with a gapped single Dirac cone electronic dispersion relation have been investigated by THz magnetophotoresponse (PR) and magnetotransport 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 twodimensional 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 magnetoresistance (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 gateinduced electric fields.

Observation of Thermoelectric Voltages from the TwoDimensional 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 (2015). 44(10) 35983602.
HgTe quantum wells (QWs) have shown a number of interesting phenomena, recently the first twodimensional topological insulating state. We have studied thermoelectric photovoltages of twodimensional 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.

Phasesensitive 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 (2015). T164 014002.
Threedimensional (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 pwave 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.

Threeterminal energy harvester with coupled quantum dots. Thierschmann, Holger; Sánchez, Rafael; Sothmann, Björn; Arnold, Fabian; Heyn, Christian; Hansen, Wolfgang; Buhmann, Hartmut; Molenkamp, Laurens W. in Nature Nanotechnology (2015). 10(10) 854858.
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 twoterminal 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 threeterminal 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 multiterminal nanoscale heat engines.

Unexpected edge conduction in mercury telluride quantum wells under broken timereversal symmetry. Ma, Eric Yue; Calvo, M. Reyes; Wang, Jing; Lian, Biao; Mühlbauer, Mathias; Brüne, Christoph; Cui, YongTao; Lai, Keji; Kundhikanjana, Worasom; Yang, Yongliang; Baenninger, Matthias; König, Markus; Ames, Christopher; Buhmann, Hartmut; Leubner, Philipp; Molenkamp, Laurens W.; Zhang, ShouCheng; GoldhaberGordon, David; Kelly, Michael A.; Shen, ZhiXun in Nature Communications (2015). 6(1)
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 timereversal 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 timereversal symmetry using microwave impedance microscopy, and compare our findings to a noninverted 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 materialspecific properties and possibly manybody effects.

Temperaturedriven 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 (2015). 91(20) 205311.
We report on a temperatureinduced transition from a conventional semiconductor to a twodimensional 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 twocarrier model. Above the onset of quantized magnetotransport at low temperature, we observe a pronounced linear magnetoresistance that develops from a classical quadratic lowfield magnetoresistance if electrons and holes coexist. Temperaturedependent bulk band structure calculations predict a transition from a conventional semiconductor to a topological insulator in the regime where the linear magnetoresistance occurs.

Nonsinusoidal CurrentPhase 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. (2015). 114(6) 066801.
We use superconducting quantum interference device microscopy to characterize the currentphase relation (CPR) of Josephson junctions from the threedimensional 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.