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 $\nu$ Majorana cones on the surface, we show that the semion-fermion topological order emerges for $\nu =2$, and more generally, $\mathrm{S}\mathrm{O}(\nu {)}_{\nu }$ topological order for all $\nu \ge 2$ and $\mathrm{S}\mathrm{p}(n{)}_n$ for $\nu =2n$.