Topological materials

Topological superconductors can support localized Majorana states at their boundaries^1,2,3,4,5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner^6,7. 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 states^{8,9,10,11,12,13,14,15,16,17,18,19,20,21}. 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.

Nature 569, 93 (2019)

Weyl semimetals are exotic materials in which electrons behave more like photons-massless particles moving at a relativistic speed. These semimetals could also lead to devices with unusual electronic and optical properties, such as a "superlens" that can improve the spatial resolution of a scanning tunneling microscope. However, it is unclear how well Weyl semimetals hold on to their bizarre properties in real disordered materials that are littered with impurities. Here, we calculate the impact of randomness on Weyl semimetals. We find that for small amounts of disorder such gapless topological semiconductors are stable, but at intermediate disorder these systems can undergo a quantum phase transition into a metallic phase, where electrons cease to behave as relativistic particles.

Intriguingly, we discover that the nature of this continuous transition is insensitive to the many (if not all) details of impurities, a phenomenon commonly referred to as superuniversality, which leaves its signature on the behavior of various observables, such as specific heat and electrical conductivity. While this concept has been discussed previously in the context of two-dimensional quantum Hall states and one-dimensional disordered quantum wires, here, we present its incarnation in three-dimensional disordered topological materials. These features combined with several other known transitions constitute the global phase diagram of disordered Weyl systems.

Our proposed stability of moderately disordered Weyl systems should encourage practical applicability of such systems in devices, while the global phase diagram should open new research frontiers exploring the arena of disordered topological phases of matter.

Phys. Rev. X 8, 031076 (2018)