Persistent current and zero-energy Majorana modes in a p-wave disordered superconducting ring

TL;DR

This paper investigates how zero-energy Majorana modes appear in a disordered p-wave superconducting ring when threaded by magnetic flux, using persistent current discontinuities as indicators, and maps the conditions for their emergence.

Contribution

It demonstrates a method to detect Majorana modes via persistent current discontinuities and maps the parameter space for their appearance in disordered rings.

Findings

Majorana modes cause observable discontinuities in persistent current.

Disorder and magnetic flux tuning enable control over Majorana mode emergence.

The study provides a mapping of conditions for Majorana modes in disordered rings.

Abstract

We discuss the emergence of zero-energy Majorana modes in a disordered finite-length p-wave one-dimensional superconducting ring, pierced by a magnetic flux $\Phi$ tuned at an appropriate value $\Phi=\Phi_*$. In the absence of fermion parity conservation, we evidence the emergence of the Majorana modes by looking at the discontinuities in the persistent current $I[\Phi]$ at $\Phi=\Phi_*$. By monitoring the discontinuities in $I[\Phi]$, we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.