$\mathbb{Z}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups

Understand

While the symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates, the extension of these approaches to the diagnosis of topological superconductors remains a major open question.

• One important new ingredient in the analysis of topological superconductivity is the presence of $\mathbb Z_2$-valued Pfaffian invariants associated with certain high-symmetry momenta.
• Such topological invariants lie beyond the conventional scope of symmetry representation theory for band structures, and as such they are nontrivial to incorporate into the systematic calculations of the symmetry indicators of band topology.
• Here, we overcome this challenge and report the full computation of the $\mathbb Z_2$-enriched symmetry indicators for superconductors in all symmetry settings.