Perturbative results for the short-range order parameter, specific heat, and resistivity of granular superconductors

The short-range order parameter, specific heat, and resistivity of a granular superconductor are calculated to lowest, nontrivial order in the Josephson coupling J. Both the short-range order parameter and the resistivity show signs of an increased phase coherence at a finite temperature in the normal state. This quasi-reentrance is enhanced by the presence of long-range Coulomb interactions, which promote Cooper-pair tunneling between grains. The specific heat of the normal state, which is directly related to the short-range order parameter, also shows evidence of this enhanced phase coherence. At zero temperature, the resistivity can be calculated analytically, with the result that the resistance threshold which separates the superconducting and normal states is independent of the Coulomb interactions. A simple argument, based on the competition between the Josephson and resistive channels, is used to explain the behavior of the minimum in the array resistivity.