The space group classification of topological band insulators

TL;DR

This paper classifies topological band insulators considering crystal lattice symmetries, revealing three main classes and identifying numerous new potential topological phases, thus broadening the understanding beyond time-reversal symmetry.

Contribution

It provides a comprehensive classification of TBIs protected by crystalline symmetries, expanding the framework beyond time-reversal symmetry and identifying new topological phases.

Findings

Three classes of topological states identified

At least 70 three-dimensional TBIs predicted

Systematic route for discovering new TBIs

Abstract

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.