Second-order topological insulators and superconductors with an order-two crystalline symmetry

TL;DR

This paper classifies second-order topological insulators and superconductors that are protected by order-two crystalline symmetries, extending previous classifications to include antiunitary symmetries and antisymmetries.

Contribution

It provides a comprehensive classification of second-order topological phases with order-two crystalline symmetries, including antiunitary and antisymmetries, building on prior bulk phase classifications.

Findings

Complete classification of second-order topological insulators and superconductors with order-two crystalline symmetries.

Extension of classification to include antiunitary symmetries and antisymmetries.

Identification of protected zero modes at corners and gapless modes at hinges in these phases.

Abstract

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys.\ Rev.\ B {\bf 90}, 165114 (2014)], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.