Three dimensional topological superconductors with time reversal symmetry (class DIII) are indexed by an integer $ν$, the number of surface Majorana cones, according to the free fermion classification. The superfluid B phase of He³ realizes the $ν=1$ phase. Recently, it has been argued that this classification is reduced in the presence of interactions to Z₁₆. This was argued from the symmetry respecting surface topological orders of these states, which provide a non-perturbative definition of the bulk topological phase. Here, we verify this conclusion by focusing on the even index case, $ν=2m$, where a vortex condensation approach can be used to explicitly derive the surface topological orders. We show a direct relation to the well known result on one dimensional topological superconductors (class BDI), where interactions reduce the free fermion classification from Z down to Z₈. Finally, we discuss in detail the fermionic analog of Kramers time reversal symmetry, which allows semions of some surface topological orders to transform as T²=± i.
No takes yet. Share an insight, caveat, or question.
Metlitski et al. (2014) studied this question.