Quantum effects and the resistive transition in superconducting granular films

Static and dynamic properties of an array of Josephson junctions shunted by Ohmic resistors are discussed within a quantum Ginzburg-Landau theory. The phase diagram at zero temperature is calculated in mean field approximation. It shows that global superconductivity atT=0 is possible only if the normal-state film resistanceR _n is smaller than a critical valueR _n ^c which depends only logarithmically on the Josephson coupling and charging energies. The particular valueR _n ^c =6.5 k found in recent experiments on granular films is in reasonable agreement with estimates for these parameters. A phenomenological order parameter relaxation mechanism is introduced and the associated fluctuation-induced conductivity and diamagnetic susceptibility aboveT _c are determined. The resulting precursor conductivity does not explain the observed exponential decrease withR _n-R _n ^c of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thousless picture, is in good agreement with the experimental data.