Higher-order topological insulators and superconductors protected by inversion symmetry

TL;DR

This paper classifies higher-order topological insulators and superconductors protected by inversion symmetry, revealing their surface states as topological defects and proposing physical realizations with controllable localized modes.

Contribution

It provides a complete classification of inversion-protected higher-order topological phases in any dimension using a layer construction approach.

Findings

Classifies inversion-protected higher-order topological phases in all dimensions.

Shows surface states as irremovable topological defects.

Proposes physical realizations with controllable localized modes.

Abstract

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We show that the surface states of higher-order topological insulators and superconductors can be thought of as globally irremovable topological defects and provide a complete classification of these inversion-protected phases in any spatial dimension for the ten symmetry classes by means of a layer construction. Furthermore, we discuss possible physical realizations of such states starting with a time-reversal invariant topological insulator (class AII) in three dimensions or a time-reversal invariant topological superconductor (class DIII) in two or three dimensions. The former can be used to build a three-dimensional second-order topological insulator which exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter enables the construction of three-dimensional third-order or two-dimensional second-order topological superconductors hosting Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.