Classification of Majorana Fermions in Two-Dimensional Topological Superconductors

TL;DR

This paper classifies Majorana Fermions in 2D topological superconductors, providing numerical evidence to distinguish different types based on topological phase transitions, advancing understanding for quantum computing applications.

Contribution

It introduces a classification scheme for Majorana Fermions in 2D systems and presents a numerical method to identify their types via topological phase transition signatures.

Findings

Identification of two Majorana Fermion types with different polygon sign rules

Numerical evidence linking Majorana classification to first order topological phase transitions

Application of the method to various 2D topological superconductors

Abstract

Recently, Majorana Fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation (TQC). They are proposed to exist in various two-dimensional (2D) topological systems, such as px+ipy topological superconductor and nanowire-superconducting hybridization system. In this paper, two types of Majorana Fermions with different polygon sign rules are pointed out. A "smoking gun" numerical evidence to identify MF's classification is presented through looking for the signature of a first order topological quantum phase transition. By using it, several 2D topological superconductors are studied.