Critical currents and voltages in weakly nonlinear inhomogeneous media

Abstract

A random mixture of two components is considered. It is assumed that both these components have current-voltage characteristics which contain weak nonlinear terms of a powerlaw type. General results for the effective nonlinear susceptibility as well as for critical current and voltage, defined as the crossovers from linear to nonlinear behaviour are obtained, both above and below the percolation threshold. They agree with the results obtained previously for some less general composites. New results for the mixture of 'nonlinear insulator'+'linear metal' are found. All these results are valid in the low-field limit. For larger fields it is shown that the exponent x describing the scaling of critical current as a function of conductance obeys the relation: x (d − 1)ν/t for a random metal-insulator composite and x 1 − ν/q for a superconductornormal conductor composite (d is dimensionality, ν is the percolation correlation length exponent and t and q are conductivity critical exponents for metal-insulator and superconductor-normal conductor percolation, respectively).