Braiding Statistics of Vortices in 2+1d Topological Superconductors from Stacking

Abstract

Class D topological superconductors in 2+1 dimensions are known to have a ℤ₁₆ classification in the presence of interactions, with 16 different topological orders underlying the 16 distinct phases. By applying the fermionic stacking law, which involves anyon condensation, on the effective Hamiltonian describing the topological interaction of vortices in the p+ip superconductor, which generates the 16 other phases, we recover the braiding coefficients of vortices for all remaining phases as well as the ℤ₁₆ group law. We also apply this stacking law to the time-reversal invariant Class DIII superconductors (which can themselves be obtained from stacking two Class D superconductors) and recover their ℤ₂ classification.