Higher-Order Topology in Bismuth

TL;DR

This paper reveals that bismuth, previously considered topologically trivial, is actually a higher-order topological insulator with protected hinge states, supported by theoretical analysis and experimental evidence.

Contribution

It demonstrates that bismuth hosts higher-order topological states, expanding the understanding of topological phases in elemental solids.

Findings

Bismuth exhibits hinge states protected by symmetry.

Experimental techniques confirm the presence of topological hinge modes.

Theoretical analysis classifies bismuth as a higher-order topological insulator.

Abstract

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature 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-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at 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.