CHARGING EFFECTS AND QUANTUM CROSSOVER IN GRANULAR SUPERCONDUCTORS

The effects of the charging energy in the superconducting transition of granular materials or Josephson junction arrays are investigated using a pseudo-spin-one model. Within a mean-field renormalization-group approach, we obtain the phase diagram as a function of temperature and charging energy. In contrast to earlier treatments, we find no sign of a reentrant transition in agreement with more recent studies. A crossover line is identified in the nonsuperconducting side of the phase diagram and along which we expect to observe anomalies in the transport and thermodynamic properties. We also study a charge ordering phase, which can appear for large nearest neighbor Coulomb interaction, and show that it leads to first-order transitions at low temperatures. We argue that, in the presence of charge ordering, a nonmonotonic behavior with decreasing temperature is possible with a maximum in the resistance just before entering the superconducting phase.