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Based on a recently developed framework, we conduct classifications oftime-reversal symmetric topological superconductors with conventional pairingsymmetries. Our real-space approach clarifies the nature of boundary modes innontrivial phases. The key difference from the calculations for topologicalcrystalline insulators originates from the appearance of vortex zero modes onthe interface of several two-dimensional topological superconductors. We findthat our classification is complete in the $K$-theory sense for all rod groups,all layer groups, and 159 out of 230 space groups. Our results shed new lighton superconductors with conventional pairing as candidates for topologicalsuperconductors.

Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries