Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells.

Two dimensional topological insulators have attracted much interest due to their potential applications in spintronics and quantum computing. To access the exotic physical phenomena, a gate electric field is required to tune the Fermi level into the bulk band gap. Hexagonal boron nitride (h-BN) is a promising alternative gate dielectric due to its unique advantages such as flat and charge-free surface. Here we present a hexagonal boron nitride/graphite van der Waals heterostructure as a top gate on HgTe heterostructure-based Hall bar devices. We compare our results to devices with h-BN/Ti/Au and HfO2/Ti/Au gates. Devices with a h-BN/graphite gate show no charge carrier density shift compared to as-grown structures, in contrast to a significant n-type carrier density increase for HfO2/Ti/Au. We attribute this observation mainly to the comparable work function of HgTe and graphite. In addition, devices with hexagonal boron nitride gate dielectric show slightly higher electron mobility compared to HfO2-based devices. Our results demonstrate the compatibility between layered materials transfer and wet-etched structures and provide a strategy to solve the issue of significant shifts of the carrier density in gated HgTe heterostructures.

Spectral Asymmetry Induces a Re-Entrant Quantum Hall Effect in a Topological Insulator.

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.

Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials.

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.

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.

Low-Temperature Atomic Layer Deposition of Hafnium Oxide for Gating Applications.

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 self-limiting 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 temperature-sensitive materials.

Counterpropagating topological and quantum Hall edge channels.

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.

Magneto-transport measurements on gated high-mobility 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 p-type 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 n-conducting topological surface states and p-conducting Volkov-Pankratov states at the relevant gate voltages.

Electron-Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator.

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.

Quantized spin Hall conductance in a magnetically doped two dimensional topological insulator.

Soon after the discovery of the quantum spin Hall effect, it has been predicted that a magnetic impurity in the presence of strong Coulomb interactions will destroy the quantum spin Hall effect. However, the fate of the quantum spin Hall effect in the presence of magnetic impurities has not yet been experimentally investigated. Here, we report the successful experimental demonstration of a quantized spin Hall resistance in HgTe quantum wells dilutely alloyed with magnetic Mn atoms. These quantum wells exhibit an inverted band structure that is very similar to that of the undoped material. Micron sized devices of (Hg,Mn)Te quantum well (in the topological phase) show a quantized spin Hall resistance of h/2e2 at low temperatures and zero magnetic field. At finite temperatures, we observe signatures of the Kondo effect due to interaction between the helical edge channels and magnetic impurities. Our work lays the foundation for future investigations of magnetically doped quantum spin Hall materials towards the realization of chiral Majorana fermions.

Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator.

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.

Dynamical Separation of Bulk and Edge Transport in HgTe-Based 2D Topological Insulators.

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.

How to measure the entropy of a mesoscopic system via thermoelectric transport.

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.

Approaching Quantization in Macroscopic Quantum Spin Hall Devices through Gate Training.

Quantum spin Hall edge channels hold great promise as dissipationless one-dimensional conductors. However, the ideal quantized conductance of 2e^{2}/h is only found in very short channels-in contradiction with the expected protection against backscattering of the topological insulator state. In this Letter we show that enhancing the band gap does not improve quantization. When we instead alter the potential landscape by charging trap states in the gate dielectric using gate training, we approach conductance quantization for macroscopically long channels. Effectively, the scattering length increases to 175 µm, more than 1 order of magnitude longer than in previous works for HgTe-based quantum wells. Our experiments show that the distortion of the potential landscape by impurities, leading to puddle formation in the narrow gap material, is the major obstacle for observing undisturbed quantum spin Hall edge channel transport.

Proximity-Induced Superconductivity in CdTe-HgTe Core-Shell Nanowires.

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 Ic Rn product, a positive excess current, and multiple Andreev reflections up to fourth order further indicate a high interface quality of the junctions.

High Mobility HgTe Microstructures for Quantum Spin Hall Studies.

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 × 103 cm2/(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.

Publisher's Note: Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates [Phys. Rev. Lett. 117, 086403 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.086403.

Electron-hole asymmetry of the topological surface states in strained HgTe.

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.

Gapless Andreev bound states in the quantum spin Hall insulator HgTe.

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.

Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates.

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-Cd_{0.5}Zn_{0.5}Te 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.

Three-terminal energy harvester with coupled quantum dots.

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.