Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries

We propose a protocol for deriving symmetry indicators that depend on a minimal set of necessary symmetry data of the bulk bands and can diagnose boundary features. Specifically, to obtain indicators manifesting clear bulk-boundary correspondence, we combine the topological crystal classification scheme in the real space and a twisted equivariant K group analysis in the momentum space. The key step is to disentangle the generally mixed strong and weak indicators through a systematic basis-matching procedure between our real-space and momentum-space approaches. We demonstrate our protocol using an example of two-dimensional time-reversal odd-parity superconductors, where the inversion symmetry is known to protect a higher-order phase with corner Majoranas. Symmetry indicators derived from our protocol can be readily applied to ab initio database and could fuel material predictions for strong and weak topological crystalline superconductors with various boundary features.