Z₂-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups

Symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates. One important new ingredient in the analysis of topological superconductivity is the presence of Z₂-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 Z₂-enriched symmetry indicators for SCs in all symmetry settings. Our framework can also be readily integrated with DFT calculations to elucidate on the possible properties of unconventional superconductivity in a given compound. As a demonstration, we analyze the interplay between pairing symmetry and topologies in the recently discovered SCs CaPtAs and CaSb₂.

SO, H.C. Po, and K. Shiozaki, arXiv:2008.05499