Anderson Localization in Degenerate Spin-Orbit Coupled Fermi Gases with Disorder

TL;DR

This paper investigates how disorder and spin-orbit coupling influence superconductivity in Fermi gases, revealing a transition to an insulating state and the formation of superconducting islands.

Contribution

It provides a detailed analysis of the interplay between disorder, spin-orbit coupling, and superconductivity using Bogoliubov-de Gennes equations, highlighting the insensitivity of the system to disorder with strong spin-orbit coupling.

Findings

Superconducting order parameter vanishes with increasing disorder while the energy gap persists.

Increasing spin-orbit coupling reduces the order parameter and energy gap at low disorder.

At high disorder, stronger spin-orbit coupling enhances the superconducting order parameter.

Abstract

Competition between superconductivity and disorder plays an essential role in understanding the metal-insulator transition. Based on the Bogoliubov-de Gennes equation, we studied an s-wave superconductor with both spin-orbit coupling and disorder are presented. With increasing the strength of disorder, the mean superconducting order parameter will vanish while the energy gap will persist, which indicates that the system undergoes a transition from a superconducting state to an insulating state. This can be confirmed by calculating the inverse participation ratio. We also find that, if the strength of disorder is small, the superconducting order parameter and the energy gap will decrease if we increase the strength of spin-orbit coupling and Zeeman field. In the large disorder limits, increasing the strength of spin-orbit coupling will increase the mean superconducting order parameter. This phenomenon shows that the system is more insensitive to disorder if the spin-orbit coupling is presented. Numerical computing also shows that the whole system breaks up into several superconducting islands instead of being superconductivity.