Effects of fluctuations and Coulomb interaction on the transition temperature of granular superconductors

TL;DR

This paper analyzes how fluctuations and Coulomb interactions suppress the superconducting transition temperature in granular metals, distinguishing between bosonic and fermionic mechanisms based on system parameters.

Contribution

It provides a detailed calculation of the transition temperature correction considering both mechanisms in 3D and film granular systems, highlighting the dominant suppression process.

Findings

Bosonic mechanism dominates when $T_c > g_T \, \delta$.

Fermionic mechanism dominates when $T_c < g_T \, \delta$.

Quantitative correction formulas for transition temperature in granular systems.

Abstract

We investigate the suppression of superconducting transition temperature in granular metallic systems due to (i) fluctuations of the order parameter (bosonic mechanism) and (ii) Coulomb repulsion (fermionic mechanism) assuming large tunneling conductance between the grains $g_{T}\gg 1$. We find the correction to the superconducting transition temperature for 3$d$ granular samples and films. We demonstrate that if the critical temperature $T_c > g_T \delta$, where $\delta$ is the mean level spacing in a single grain the bosonic mechanism is the dominant mechanism of the superconductivity suppression, while for critical temperatures $T_c < g_T \delta$ the suppression of superconductivity is due to the fermionic mechanism.