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Topological Mirror Superconductivity

We demonstrate the existence of topological superconductors (SC) protected by mirror and time reversal (TR) symmetries. D-dimensional (D=1,2,3) crystalline SCs are characterized by 2^(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z_2 index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa, and that a DIII SC with a mirror plane is always TR trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.