Fidelity Approach in Topological Superconductors with Disorders

TL;DR

This paper uses the fidelity approach to investigate how disorders affect topological superconductivity in a nanowire system, revealing multiple peaks in fidelity susceptibility related to phase transitions and Majorana state pinning.

Contribution

It introduces the fidelity susceptibility as a tool to detect topological phase transitions and disorder effects in superconducting nanowires.

Findings

Major peak indicates topological quantum phase transition

Additional peaks signal Majorana state pinning by disorders

Fidelity susceptibility effectively characterizes disorder effects

Abstract

We apply the fidelity approach to study the topological superconductivity in a spin-orbit coupled nanowire system. The wire is modeled as a one layer lattice chain with Zeeman energy and spin-orbit coupling, which is in proximity to a multi layer superconductor. In particular, we study the effects of disorders and find that the fidelity susceptibility show multiple peaks. It is revealed that the major peak indicates the topological quantum phase transition, while other peaks signal the pining of the Majorana bound states by disorders.