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

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⪢1. We find the correction to the superconducting transition temperature for 3d granular samples and films. We demonstrate that if the critical temperature T_c>g_Tδ, where δ 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_Tδ the suppression of superconductivity is due to the fermionic mechanism.