Reduction of electron repulsion and enhancement of $T_{c}$ in small diffusive superconducting grains

TL;DR

This paper proposes that in small disordered superconducting grains, the Coulomb repulsion is weakened, leading to an increase in the critical temperature, contrasting with the suppression observed in larger two-dimensional systems.

Contribution

The study introduces a mechanism where finite size effects reduce Coulomb repulsion, resulting in enhanced superconducting transition temperatures in small grains.

Findings

Coulomb repulsion is effectively weakened in small grains.

Small grains show an increase in $T_{c}$ due to finite size effects.

The mechanism adds to the known density of states effects on $T_{c}.

Abstract

The superconducting properties of small metallic grains has been a topic of active research for half a century now. Early experiments demonstrated a remarkable rise in the critical temperature, $T_{c}$, with reducing grain size in a variety of materials. In two dimensional diffusive superconductors, $T_{c}$ is decreased due to enhanced Coulomb repulsion. We propose that in finite size grains, the diffusive enhancement of the Coulomb repulsion is weakened and leads ultimately to an increase in $T_{c}$ in isolated, disordered two dimensional grains. Our mechanism is superimposed on the possible enhancement in $T_{c}$ due to the change in the density of states of finite size systems.