Christoph Brüne

Quantum Spin Hall Insulator State in HgTe Quantum Wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e2/h, where e is the electron charge and h is Plancks constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field–induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

Nonlocal Transport in the Quantum Spin Hall State

Living on the Edge Topological insulators are a recently described state of matter in which the bulk material is an insulator but with a metallic surface state that is protected by the topology of the Fermi surface. Roth et al. (p. 294; see the Perspective by Büttiker) now show that the current flow on the surface takes place in edge states around the boundary of the sample. These are similar to the current transport in high-quality two-dimensional electron gases in high magnetic field, which confirms theoretical work on these materials. A topological insulator exhibits current flow in edge states around the sample without the need for magnetic fields. Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.

Spin polarization of the quantum spin Hall edge states

The quantum spin Hall state is predicted to consist of two oppositely polarized spin currents travelling in opposite directions around the edges of a topological insulator. Non-local measurements of the transport in HgTe quantum wells confirm the polarized nature of these edge states.

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.

Induced superconductivity in the quantum spin Hall edge

Majorana fermions, which are their own antiparticles, are expected to exist in topological superconductors. A study using superconducting leads in contact with a quantum well reveals the presence of supercurrents along one-dimensional sample edges of a quantum spin Hall state. These edge supercurrents are topological.

4π-periodic Josephson supercurrent in HgTe-based topological Josephson junctions.

The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4π-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4π-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator.

Surface State Charge Dynamics of a High-Mobility Three-Dimensional Topological Insulator

We present a magneto-optical study of the three-dimensional topological insulator, strained HgTe, using a technique which capitalizes on advantages of time-domain spectroscopy to amplify the signal from the surface states. This measurement delivers valuable and precise information regarding the surface-state dispersion within <1 meV of the Fermi level. The technique is highly suitable for the pursuit of the topological magnetoelectric effect and axion electrodynamics.

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.

Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry.

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 time-reversal 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 time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted 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 material-specific properties and possibly many-body effects.

Josephson Supercurrent through the Topological Surface States of Strained Bulk HgTe

enable a study of transport through its unconventional surface states without being hindered by a parallel bulk conductance. Here, we show transport experiments on HgTe-based Josephson junctions to investigate the appearance of the predicted Majorana states at the interface between a topological insulator and a superconductor. Interestingly, we observe a dissipationless supercurrent flow through the topological surface states of HgTe. The current-voltage characteristics are hysteretic at temperatures below 1 K, with critical supercurrents of several microamperes. Moreover, we observe a magnetic-field-induced Fraunhofer pattern of the critical supercurrent, indicating a dominant 2� -periodic Josephson effect in the unconventional surface states. Our results show that strained bulk HgTe is a promising material system to get a better understanding of the Josephson effect in topological surface states, and to search for the manifestation of zero-energy Majorana states in transport experiments.