Noise and crossover exponents in conductor-insulator mixtures and superconductor-conductor mixtures

Abstract

The resistance noise of random conductor-insulator mixtures is studied in the case where the insulators have a small but finite conductance. The conductance noise of superconductor-conductor mixtures is similarly studied when the superconductors have a small but finite resistance. The Migdal-Kadanoff renormalization-group calculations that lead to the appropriate linear and nonlinear scaling fields for these problems are discussed in detail. The corresponding homogeneity relations for the total noise are valid near the unstable percolation fixed point whatever the relative size of the microscopic noises. The exponents of the superconductor-conductor mixture appear naturally in the scaling form of the noise coming from the imperfect insulators. Analogously, the exponents of the conductor-insulator mixture enter in the scaling form of the noise coming from the imperfect superconductors in the superconductor-conductor problem. Monte Carlo simulations in two and three dimensions confirm that the scaling predictions are valid well beyond the domain of applicability of the Migdal-Kadanoff approach. For all multifractal moments and both types of mixtures, there is a single crossover exponent and a single correlation length associated with the ratio of the microscopic conductances.

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