Topology in time-reversal symmetric crystals

TL;DR

This paper introduces a new counting algorithm to classify topological invariants in time-reversal symmetric crystals, unifying known invariants, predicting new phases, and providing a comprehensive framework for 2D and 3D materials.

Contribution

It presents a unified, efficient method to classify all topological invariants in time-reversal symmetric crystals, revealing new phases and invariants.

Findings

Unified classification of topological invariants in 2D materials

Prediction of new topological phases and invariants

A straightforward procedure for 3D crystal analysis

Abstract

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are used to label distinct types of topological insulators. But it is not generally known how many or which invariants can exist in any given crystalline material. Using a new and efficient counting algorithm, we study the topological invariants that arise in time-reversal symmetric crystals. This results in a unified picture that explains the relations between all known topological invariants in these systems. It also predicts new topological phases and one entirely new topological invariant. We present explicitly the classification of all two-dimensional crystalline fermionic materials, and give a straightforward procedure for finding the analogous result in any three-dimensional structure. Our study represents a single, intuitive physical picture applicable to all topological invariants in real materials, with crystal symmetries.