Topological classification and diagnosis in magnetically ordered electronic materials

TL;DR

This paper provides a comprehensive topological classification of magnetically ordered electronic materials based on magnetic space group symmetries, revealing new topological invariants and surface states.

Contribution

It offers the first exhaustive classification of 3D magnetic topological insulators for all 1421 magnetic space groups and maps symmetry representations to topological invariants.

Findings

Classified all 3D magnetic topological insulators by magnetic space groups

Computed symmetry-based indicators for each topological class

Established a complete mapping from symmetry to topological invariants

Abstract

We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states. We obtain, by explicit and exhaustive construction, the topological classification of electronic band insulators that are magnetically ordered for each one of the 1421 magnetic space groups in three dimensions. We have also computed the symmetry-based indicators for each nontrivial class, and, by doing so, establish the complete mapping from symmetry representations to topological invariants.