Diamagnetism of percolative granular superconductors and diluted Josephson arrays.

Abstract

We discuss diamagnetic fluctuations in percolative granular superconductors modeled by randomly diluted Josephson arrays in which junctions are present with probability p and absent with probability 1-p. Results are obtained using mean-field theory and scaling arguments, which provide a qualitative picture for two- and three-dimensional granular materials. Asymptotically exact critical exponents are obtained in an epsilon expansion about d = 6-epsilon dimensions. In zero external field, the singular part of the average diamagnetic susceptibility of finite clusters at zero temperature is proportional to chemically bondp-p/sub c/chemically bond/sup t-2//sup ..nu../, where t is the exponent controlling the growth of the macroscopic conductivity in diluted resistor networks and ..nu.. is the percolation correlation length exponent. In nonzero external magnetic field, the disordered Josephson network exhibits spin-glassy behavior, and the singular part of the mean-square fluctuation in the magnetic moment of finite clusters is proportional to chemically bondp-p/sub c/chemically bond/sup t>2/-2..nu..$, where t/sub 2/ = (d-2)..nu..+phi/sub 2/ and phi/sub 2/ is a crossover exponent associated with the square of the temperature. We evaluate phi/sub 2/ to first order in epsilon and find it to be identical to an exponent describing corrections to scaling in the probability distribution for the resistance of a dilutedmore » resistor network at the percolation threshold, i.e., phi/sub 2/ = 1+0(epsilon/sup 2/).« less