Enhanced, phase coherent, multifractal-like, two-dimensional superconductivity

TL;DR

This paper investigates how disorder affects two-dimensional superconductivity, revealing that weak disorder can enhance superconductivity and produce multifractal spatial features, while phase coherence persists until the transition to an insulator.

Contribution

It provides a numerical study of 2D superconductivity under disorder, highlighting the multifractal nature and phase coherence behavior in the weak to moderate disorder regime.

Findings

Superconductivity is enhanced by weak disorder.

The order parameter exhibits multifractal-like spatial distribution.

Phase coherence persists until the disorder induces an insulating state.

Abstract

We study the interplay of superconductivity and disorder by solving numerically the Bogoliubov-de-Gennes equations in a two dimensional lattice of size $80\times80$ which makes possible to investigate the weak-coupling limit. In contrast with results in the strong coupling region, we observe enhancement of superconductivity and intriguing multifractal-like features such as a broad log-normal spatial distribution of the order parameter, a parabolic singularity spectrum, and level statistics consistent with those of a disordered metal at the Anderson transition. The calculation of the superfluid density, including small phase fluctuations, reveals that, despite this intricate spatial structure, phase coherence still holds for sufficiently weak disorder. It only breaks down for stronger disorder but before the insulating transition takes place.