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

TL;DR

This paper numerically investigates the entanglement spectrum of two-dimensional fermionic paired states that break parity and time-reversal symmetries, revealing non-Abelian topological order in the weak-pairing phase and Abelian order in the strong-pairing phase.

Contribution

It provides a numerical analysis of the entanglement spectrum in 2D fermionic paired states, identifying signatures of non-Abelian topological order through Majorana zero modes.

Findings

Majorana zero mode appears in weak-pairing phase

No Majorana mode in strong-pairing phase

Distinction between non-Abelian and Abelian topological orders

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.