Short range and long range phase coherence in granular superconductors

The Josephson phase model with charging energies is studied in the Oguchi pair approximation. Allowing for the short-range fluctuations of the phase eliminates the reentrant feature predicted by some previous treatments. We find, however, a fluctuating tendency to reentrance in the sense that, for Josephson coupling strengths below the threshold value, the phase short-range-order in the disordered phase reaches its maximum at a finite temperature. We suggest that this might be the explanation of effects like the resistance minimum seen in granular Sn samples. We make detailed comparison between the de Gennes pseudospin model and various other truncation schemes for the phase Hamiltonian.