Topological classification and diagnosis in magnetically ordered electronic materials

Understand

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.