Physical Review Research

A striking feature of three-dimensional (3D) topological insulators (TIs) is the theoretically expected topological magnetoelectric (TME) effect, which gives rise to additional terms in Maxwell's laws of electromagnetism with an universal quantized coefficient proportional to half-integer multiples of the fine-structure constant α. In an ideal scenario one therefore expects also quantized contributions in the magnetooptical response of TIs. We review this premise by taking into account the trivial dielectric background of the TI bulk and potential host substrates, and the often present contribution of itinerant bulk carriers. We show (i) that one obtains a nonuniversal magnetooptical response whenever there is impedance mismatch between different layers and (ii) that the detectable signals due to the TME rapidly approach vanishingly small values as the impedance mismatch is detuned from zero. We demonstrate that it is methodologically impossible to deduce the existence of a TME exclusively from an optical experiment in the thin film limit of 3D TIs at high magnetic fields.

Journal of Applied Physics

We present a setup for fast, low-bias ( ≤ 1 mV) DC transport measurements with μs time resolution for high ohmic resistance ( ≈ 20 k Ω) 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.

ACS Photonics

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.

Physical Review Research

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of nonlinearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a nonlinear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the nonlinear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state, which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the nonlinear regime, where the cnoidal eccentricity decreases from edge to bulk.

Nature Communications

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.