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.

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.

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.

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.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions.

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Universality and Stability of the Edge States of Chiral-Symmetric Topological Semimetals and Surface States of the Luttinger Semimetal.

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by chiral symmetry and characterized by the topological winding number N. We derive the asymptotic chiral-symmetric boundary conditions and find that there are N+1 universal classes of them. The class determines the numbers of flatband edge states on either side off the node in the 1D spectrum and the winding number N gives the total number of edge states. We then show that the edge states of chiral nodal semimetals are robust: they persist in a finite-size stability region of parameters of chiral-asymmetric terms. This significantly extends the notion of 2D and 3D topological nodal semimetals. We demonstrate that the Luttinger model with a quadratic node for j=3/2 electrons is a 3D topological semimetal in this new sense and predict that α-Sn, HgTe, possibly Pr_{2}Ir_{2}O_{7}, and many other semimetals described by it are topological and exhibit surface states.

Tunneling Planar Hall Effect in Topological Insulators: Spin Valves and Amplifiers.

We investigate tunneling across a single ferromagnetic barrier on the surface of a three-dimensional topological insulator. In the presence of a magnetization component along the bias direction, a tunneling planar Hall conductance (TPHC), transverse to the applied bias, develops. Electrostatic control of the barrier enables a giant Hall angle, with the TPHC exceeding the longitudinal tunneling conductance. By changing the in-plane magnetization direction, it is possible to change the sign of both the longitudinal and transverse differential conductance without opening a gap in the topological surface state. The transport in a topological-insulator-ferromagnet junction can, thus, be drastically altered from a simple spin valve to an amplifier.

Accessing topological superconductivity via a combined STM and renormalization group analysis.

The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.

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.

Proposal for an all-electrical detection of crossed Andreev reflection in topological insulators.

Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator-superconductor (SC)-quantum spin Hall insulator junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a five-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.

Induced superconductivity in the three-dimensional topological insulator HgTe.

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.