Superconductivity of disordered Dirac fermions in graphene

TL;DR

This study numerically investigates how disorder influences superconductivity in graphene with attractive interactions, revealing that weak disorder can enhance superconductivity near the critical interaction strength, contrary to the usual suppressive effect of disorder.

Contribution

It demonstrates that in disordered graphene, weak disorder can enhance superconductivity and mesoscopic inhomogeneities play a significant role, providing insights beyond mean-field theories.

Findings

Weak disorder enhances superconductivity below the critical interaction strength.

Strong disorder suppresses superconductivity, consistent with conventional understanding.

Mesoscopic inhomogeneities significantly boost superconductivity in the weak disorder regime.

Abstract

We numerically study the interplay between superconductivity and disorder on the graphene honeycomb lattice with on-site Hubbard attractive interactions U using a spatially inhomogeneous self-consistent Bogoliubov-de Gennes (BdG) approach. In the absence of disorder there are two phases at charge neutrality. Below a critical value Uc for attractive interactions there is a Dirac semimetal phase and above it there is a superconducting phase. We add scalar potential disorder to the system, while remaining at charge neutrality on average. Numerical solution of the BdG equations suggests that while in the strong attraction regime (U > Uc) disorder has the usual effect of suppressing superconductivity, in the weak attraction regime (U < Uc) weak disorder enhances superconductivity. In the weak attraction regime, disorder that is too strong eventually suppresses superconductivity, i.e., there is an optimal disorder strength that maximizes the critical temperature Tc. Our numerical results also suggest that in the weakly disordered regime, mesoscopic inhomogeneities enhance superconductivity significantly more than what is predicted by a spatially uniform mean-field theory a` la Abrikosov-Gorkov. In this regime, superconductivity consists of rare phase-coherent superconducting islands. We also study the enhancement of the superconducting proximity effect by disorder and mesoscopic inhomogeneities, and obtain typical spatial plots of the tunneling density of states and the superfluid susceptibility that can be directly compared to scanning tunneling miscroscopy (STM) experiments on proximity-induced superconductivity in graphene.