Verifying Non-Abelian Statistics by Numerical Braiding Majorana Fermions

TL;DR

This paper proposes a numerical approach to verify the non-Abelian statistics of Majorana fermions in topological superconductors by analyzing braiding operators within a single particle framework.

Contribution

It introduces a novel single particle representation of braiding operators to verify non-Abelian statistics of Majorana fermions in 1D and 2D topological superconductors.

Findings

Verified non-Abelian statistics of MFs in 1D and 2D systems

Established a relationship between braiding operators and BdG states

Provided a numerical method for experimental verification

Abstract

Recently, Majorana fermions (MFs) have attracted intensive attention because of their possible non-Abelian statistics. This paper points out an approach to verify the non-Abelian statistics of MFs in topological superconductors. We introduce a single particle representation of braiding operators that obey anti-commutating relation of Bogolubov-de Gennes (BdG) states. From the relationship between the braiding operator of MFs and that of BdG states, we verify non-Abelian statistics of MFs in 1D and 2D topological SCs.