Braiding statistics and classification of two-dimensional charge- 2m superconductors

Abstract

© 2016 American Physical Society. We study braiding statistics between quasiparticles and vortices in two-dimensional charge-2m (in units of e) superconductors that are coupled to a Z2m dynamical gauge field, where m is any positive integer. We show that there exist 16m types of braiding statistics when m is odd, but only 4m types when m is even. Based on the braiding statistics, we obtain a classification of topological phases of charge-2m superconductors - or formally speaking, a classification of symmetry-protected topological phases, as well as invertible topological phases, of two-dimensional gapped fermions with Z2mf symmetry. Interestingly, we find that there is no nontrivial fermionic symmetry-protected topological phase with Z4f symmetry.