Helene Bouchiat

The topology of WTe 2 , a transition-metal dichalcogenide with large spin-orbit interactions, is thought to combine type II Weyl semimetal and second-order topological insulator (SOTI) character. The SOTI character should endow WTe 2 multilayer crystals with topologically protected helical states at their hinges, and, indeed, one-dimensional states have been detected thanks to Josephson interferometry. However, the immunity to backscattering conferred to those states by their helical nature has so far not been tested. To probe the topological protection of WTe 2 edge states, we have fabricated superconducting quantum interference devices (SQUIDs) in which the supercurrent through a junction on the crystal edge interferes with the supercurrent through a junction in the bulk of the crystal. We find behaviors ranging from a symmetric SQUID to asymmetric SQUID patterns, including one in which the modulation by magnetic field reveals a sawtoothlike supercurrent versus phase relation for the edge junction, demonstrating that the supercurrent at the edge is carried by ballistic channels over 600 nm, a telltale sign of the SOTI character of multilayer WTe 2 .

We investigate quantum transport in micrometer-sized single crystals of Bi 4 Br 4 , a material predicted to be a second-order topological insulator. 1D topological states with long phase coherence times are revealed via the modulation of quantum interference with magnetic field and gate voltage. In particular, we demonstrate the existence of Aharonov-Bohm interference between 1D ballistic states several micrometers long, that we identify as phase-coherent hinge modes on neighboring step edges at the crystal surface. These Aharonov-Bohm oscillations are made possible by a disordered phase-coherent contact region, the existence of which is confirmed by scanning transmission electron microscopy combined with energy-dispersive x-ray spectroscopy (STEM-EDX) of FIB lamellae. Their coherent nature modulates the transmission of the 1D edge states, leading to weak antilocalization and universal conductance fluctuations with surprisingly large characteristic fields and a strongly anisotropic behavior. These complementary experimental results provide a comprehensive, coherent description of quantum transport in Bi 4 Br 4 and establish the material as a second-order topological insulator with topologically protected 1D ballistic states.

Detecting orbital magnetism: Graphene’s electronic structure has been predicted to lead to an unusual orbital response to magnetic fields. However, detecting this orbital magnetism is difficult because it is usually masked by the signal stemming from spins. Vallejo Bustamante et al . managed to capture this response by placing two giant magnetoresistance detectors below a sample of graphene sandwiched by layers of hexagonal boron nitride. These detectors picked up a strong diamagnetic response from an undoped sample, consistent with theoretical predictions. The technique may be useful in the investigation of other two-dimensional materials. —JS

We demonstrate enhanced robustness of the supercurrent through graphene-based Josephson junctions in which strong spin-orbit interactions (SOIs) are induced. We compare the persistence of a supercurrent at high magnetic fields between Josephson junctions with graphene on hexagonal boron-nitride and graphene on WS$_2$, where strong SOIs are induced via the proximity effect. We find that in the shortest junctions both systems display signatures of induced superconductivity, characterized by a suppressed differential resistance at a low current, in magnetic fields up to 1 T. In longer junctions however, only graphene on WS$_2$ exhibits induced superconductivity features in such high magnetic fields, and they even persist up to 7 T. We argue that these robust superconducting signatures arise from quasi-ballistic edge states stabilized by the strong SOIs induced in graphene by WS$_2$.

The mathematical field of topology has become a framework in which to describe the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk–boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principles calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunnelling spectroscopy, we probe the signatures of the rotational symmetry of the one-dimensional states located at the step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.