Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors

We construct microscopic Hamiltonians for symmetry-preserving topologically ordered states on the surface of topological crystalline superconductors, protected by a $mathbb{Z}_2$ reflection symmetry. Starting from $ u$ Majorana cones on the surface, we show that the semion-fermion topological order emerges for $ u=2$, and more generally, $mathrm{SO}( u)_ u$ topological order for all $ ugeq 2$ and $mathrm{Sp}(n)_n$ for $ u=2n$.