Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors

TL;DR

This paper develops microscopic models for surface topological orders in topological crystalline superconductors, revealing specific topological orders that depend on the number of Majorana cones and symmetry considerations.

Contribution

It constructs explicit Hamiltonians for symmetry-preserving surface topological orders in topological crystalline superconductors, identifying new orders for various numbers of Majorana cones.

Findings

Semion-fermion topological order for ν=2

SO(ν)_ν topological order for ν≥2

Sp(n)_n topological order for ν=2n

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 $\nu=2n$.