Majorana modes in solid state systems and its dynamics

TL;DR

This paper reviews Majorana modes in solid state systems, highlighting their unique properties and differences from particle physics, and discusses their existence, dynamics, and implications using theoretical models.

Contribution

It introduces a new definition of Majorana modes in solid state systems and analyzes their properties and dynamics within this framework.

Findings

Only one Majorana mode can exist in a system, at edges or in the bulk.

Majorana modes can be found both at edges and in the bulk.

The dynamical behavior of Majorana modes is characterized within the proposed framework.

Abstract

We review the properties of Majorana fermions in particle physics and point out that Majorana modes in solid state systems are significantly different. The key reason is the concept of anti-particle in solid state systems is different from its counterpart in particle physics. We define Majorana modes as the eigenstates of Majorana operators and find that they can exist both at edges and in the bulk. According to our definition, only one single Majorana mode can exist in a system no matter at edges or in the bulk. Kitaev's spinless $p$-wave superconductor is used to illustrate our results and the dynamical behavior of the Majorana modes.