CROSSOVER ELECTRIC-FIELD IN PERCOLATING PERFECT-CONDUCTOR NONLINEAR-NORMAL-METAL COMPOSITES

The nonlinear response is studied in a two-component composite with concentration p of perfect conductor (S) and concentration (I -p) of normal metal (N) with nonlinear response of the form J = sigma (A)E + chi(A) \E\2E. Below the percolation threshold p(c) of the perfect conductor, the response of the composite can be represented by [J] = sigma(e) [E] + chi(e)\[E]\2[E], where [ ... ] represents spatial averages. The magnitude of the crossover field \E(c)\, defined as the electric field at which the linear and nonlinear response of the composite become comparable, is found to have a power-law dependence \E(c)\ approximately (p(c) - p)M as the percolation threshold is approached from below. Within the effective-medium approximation, the exponent M is found to be 1/2 for all spatial dimensions. By relating the cubic nonlinear composite problem to the noise problem in linear composites, the exponent M is found to be M = (kappa' + s)/2, where kappa' and s are the noise and conductivity exponents in a S/N composite, respectively. Previously derived bounds on the noise exponent kappa' thus lead to bounds on the exponent M.