Topological superconductivity in a phase-controlled Josephson junction.

Topological superconductors can support localized Majorana states at their boundaries1-5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8-21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

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 h-BN/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 h-BN 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.

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.

Finite Field Transport Response of a Dilute Magnetic Topological Insulator-Based Josephson Junction.

Hybrid samples combining superconductors with magnetic topological insulators are a promising platform for exploring exotic new transport physics. We examine a Josephson junction of such a system based on the dilute magnetic topological insulator (Hg,Mn)Te and the type II superconductor MoRe. In the zero and very low field limits, to the best of our knowledge, the device shows, for the first time, an induced supercurrent through a magnetically doped semiconductor, in this case, a topological insulator. At higher fields, a rich and hysteretic magnetoresistance is revealed. Careful analysis shows that the explanation of this behavior can be found in magnetic flux focusing stemming from the Meissner effect in the superconductor, without invoking any role of proximity-induced superconductivity. The phenomena is important because it will ubiquitously coexist with any exotic new physics that may be present in this class of devices.

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.

Super-Resonant Transport of Topological Surface States Subjected to In-Plane Magnetic Fields.

Magnetic oscillations of Dirac surface states of topological insulators are typically expected to be associated with the formation of Landau levels or the Aharonov-Bohm effect. We instead study the conductance of Dirac surface states subjected to an in-plane magnetic field in the presence of a barrier potential. Strikingly, we find that, in the case of large barrier potentials, the surface states exhibit pronounced oscillations in the conductance when varying the magnetic field, in the absence of Landau levels or the Aharonov-Bohm effect. These novel magnetic oscillations are attributed to the emergence of super-resonant transport by tuning the magnetic field, in which many propagating modes cross the barrier with perfect transmission. In the case of small and moderate barrier potentials, we identify a positive magnetoconductance due to the increase of the Fermi surface by tilting the surface Dirac cone. Moreover, we show that for weak magnetic fields, the conductance displays a shifted sinusoidal dependence on the field direction with period π and phase shift determined by the tilting direction with respect to the field direction. Our predictions can be applied to various topological insulators, such as HgTe and Bi_{2}Se_{3}, and provide important insights into exploring and understanding exotic magnetotransport properties of topological surface states.

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.

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.

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.

Survival of the Quantum Anomalous Hall Effect in Orbital Magnetic Fields as a Consequence of the Parity Anomaly.

Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates the Onsager relation, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with σ_{xy}=-e^{2}/h to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.

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.

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.

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.

Nonsinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe.

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.

Imaging currents in HgTe quantum wells in the quantum spin Hall regime.

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.

Spin texture of Bi2Se3 thin films in the quantum tunneling limit.

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 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.

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.