Quantum effects and the resistive transition in superconducting granular films

Abstract

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 at T = 0 is possible only if the normal-state film resistance R/sub n/ is smaller than a critical value R/sub n//sup c/ which depends only logarithmically on the Josephson coupling and charging energies. The particular value R/sub n//sup c/ = 6.5 k..cap omega.. 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 above T/sub c/ are determined. The resulting precursor conductivity does not explain the observed exponential decrease with R/sub n/-R/sub n//sup c/ of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thouless picture, is in good agreement with the experimental data.