Atomic limit and inversion-symmetry indicators for topological superconductors

Symmetry indicators allow to identify topological crystalline insulators using symmetry-group analysis of their Bloch states. An extension of this approach to superconducting systems requires defining an appropriate atomic limit for superconductors. Here, we introduce such a notion of atomic limit and derive a symmetry indicator for inversion-symmetric superconductors. This indicator allows for a refined topological classification including higher-order phases for systems in the superconducting phase with and without time-reversal symmetry. We further elucidate their bulk-boundary correspondence using Dirac surface theories. This indicator is well suited for a search of topological superconductors using first-principles calculations.