Majorana Bound States and Disclinations in Topological Crystalline Superconductors

We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in topological crystalline superconductors (TCS). We first establish a complete topological classification of TCS using the Chern invariant and a few integral rotation invariants. By analytically and numerically studying disclinations, we algebraically deduce a Z$_2$-index that identifies the parity of the number of Majorana zero-modes at a disclination. Surprisingly, we also find weakly-protected Majorana fermions bound at the corners of superconductors with trivial Chern and weak invariants.