Detecting topological phases via survival probabilities of edge Majorana fermions

TL;DR

This paper studies how the survival probabilities of edge Majorana fermions can be used to identify and distinguish different topological phases and phase transitions in one-dimensional models like Kitaev and SSH models.

Contribution

It provides analytical expressions for survival probabilities in certain models and numerically characterizes topological phases using these probabilities in more general cases.

Findings

Different topological phases correspond to distinct zero points of survival probabilities.

Survival probabilities can distinguish between SSH-like topological, topological superconductor, and trivial phases.

Numerical results confirm the correlation between survival probabilities and topological phases.

Abstract

We investigate the evolutions of edge Majorana fermions (MFs) and unveil that they can be used to char- acterize different topological phases and study the topological phase transitions. For some limiting cases of the evolution process for the one-dimensional Kitaev model and Su-Schrieffer-Heeger (SSH) model, we give analytical expressions of the survival probabilities of the edge MFs, which indicates that different topological phases correspond to different zero point numbers of the defined survival probabilities at some times. For a general case, we consider a dimerized Kitaev model and the Kitaev chain with disorder chemical potential and numerically calculate the survival probabilities of two edge correlation MFs. Our results show that both of them equal to zero, one of them equals to zero at some times or neither of them equal to zero correspond to the SSH-like topological, topological superconductor and trivial phases respectively.