Quantum Critical Phenomena in Charged Superconductors

We study the effect of Coulomb interactions on the onset of superconductivity with increasing intergrain coupling in granular systems at $T=0\mathrm{}$. We show that in three dimensions (3D) the onset transition is described by Euclidean scalar electrodynamics, and so can be either first or second order, depending on parameters. A renormalization-group analysis indicates that in 2D the transition can either be first order, or second order with $3\mathrm{D}-\mathrm{XY}$-like critical behavior. In 1D Coulomb forces are shown to destroy the superconducting state.