Higher-Order Topological Insulators

TL;DR

This paper introduces higher-order topological insulators that have protected hinge states instead of surface states, classified by new topological invariants, and identifies real materials that exhibit these properties.

Contribution

It extends the concept of topological insulators to include systems with hinge states protected by spatio-temporal symmetries, providing topological invariants and experimental proposals.

Findings

Identification of chiral and helical higher-order topological insulators.

Topological invariants for both classes are established.

Materials like SnTe and modified Bi compounds are predicted as higher-order topological insulators.

Abstract

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is $\mathbb{Z}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $\mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.