Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors

Abstract

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, $\mathrm{SO}(\nu)_\nu$ topological order for all $\nu\geq 2$ and $\mathrm{Sp}(n)_n$ for $\nu=2n$.