Topological order in paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries

Abstract

We numerically evaluate the entanglement spectrum (singular value decomposition of the wavefunction) of paired states of fermions in two dimensions that break parity and time-reversal symmetries, focusing on the spin-polarized $p_x+ip_y$ case. The entanglement spectrum of the weak-pairing (BCS) phase contains a Majorana zero mode, indicating non-Abelian topological order. In contrast, for the strong-pairing (BEC) phase, we find no such mode, consistent with Abelian topological order.