Fidelity in topological superconductors with end Majorana fermions

TL;DR

This paper introduces a formalism using fidelity susceptibility to detect topological quantum phase transitions in superconductors with Majorana fermions, demonstrating robustness against certain disorders.

Contribution

It establishes a general method to calculate fidelity susceptibility from Bogoliubov-de Gennes equations for topological superconductors with Majorana fermions.

Findings

Fidelity susceptibility peaks at the topological phase transition point.

Disorders can shift the phase transition point but do not eliminate the transition.

Topological quantum phase transition is robust to various disorders.

Abstract

Fidelity and fidelity susceptibility are introduced to investigate the topological superconductors with end Majorana fermions. A general formalism is established to calculate the fidelity and fidelity susceptibility by solving Bogoliubov-de Gennes equations. It is shown that the fidelity susceptibility manifest itself as a peak at the topological quantum phase transition point for homogeneous Kitaev wire, thus serves as a valid indicator for the topological quantum phase transition which signals the appearance of Majorana fermions. The effect of disorders is investigated within this formalism. We consider three disordered systems and observe fidelity susceptibility peak in all of them. By analyzing the susceptibility peak, we notice that the local potential disorders and the hopping disorders can shift the phase transition point, while off-diagonal disorders have no obvious influence. Our results confirm that the existence of topological quantum phase transition is robust to these disorders, while the behavior of the phase transition might be influenced by disorders.