Role of long-range Coulomb interactions in granular superconductors

This paper uses the self-consistent phase-phonon approximation to study the effect of long-range Coulomb interactions in a superconducting array. We find that crucial features of the results of mean-field theory are confirmed: long-range interactions enhance the superconducting state and lower the critical value of the grain diameter, below which superconductivity is impossible. However, the reentrant phase transition found in the mean-field solution is absent from the self-consistent results. This may be because the self-consistent approximation is invalid when the superconducting state is suppressed and phase fluctuations are large, such as in the reentrant regime of the mean-field theory