We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal 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 ${\mathbb{Z}}_2$ 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 time-reversal 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.

• Received 27 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.056403