Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets
Abstract
Three dimensional topological superconductors with time reversal symmetry (class DIII) are indexed by an integer $\nu$, the number of surface Majorana cones, according to the free fermion classification. The superfluid B phase of He$^3$ realizes the $\nu=1$ phase. Recently, it has been argued that this classification is reduced in the presence of interactions to Z$_{16}$. This was argued from the symmetry respecting surface topological orders of these states, which provide a nonperturbative definition of the bulk topological phase. Here, we verify this conclusion by focusing on the even index case, $\nu=2m$, 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 Z$_8$. Finally, we discuss in detail the fermionic analog of Kramers time reversal symmetry, which allows semions of some surface topological orders to transform as $T^2=\pm i$.
 Publication:

arXiv eprints
 Pub Date:
 June 2014
 arXiv:
 arXiv:1406.3032
 Bibcode:
 2014arXiv1406.3032M
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 36 pages, 1 figure