Symmetry Indicators for Topological Superconductors

Having in mind that the symmetry-indicator theory for insulators has succeeded in extensively discovering topological insulator candidates, it is natural to think that a generalization of the theory to superconductors could facilitate the investigation of realistic topological superconductors. Since Bogoliubov quasiparticle spectra can be regarded as band structures, one might think that symmetry-indicator theory for insulators could be directly applied to Bogoliubov quasiparticle spectra. However, such a naive application has two main problems: (i) the absence of well-known symmetry-indicator formulas using \(\mathbb {Z}_2\) -valued Pfaffian invariants; (ii) the absence of nontrivial symmetry indicators for one-dimensional topological phases. In this chapter, we resolve these problems and establish symmetry-indicator theory for superconductors.