Nonlinear AC resistivity in s-wave and d-wave disordered granular superconductors

Abstract

We model s-wave and d-wave disordered granular superconductors with a three-dimensional lattice of randomly distributed Josephson junctions with finite self-inductance. The nonlinear ac resistivity of these systems was calculated using Langevin dynamical equations. The current amplitude dependence of the nonlinear resistivity at the peak position is found to be a power law characterized by exponent $\alpha$. The later is not universal but depends on the self-inductance and current regimes. In the weak current regime $\alpha$ is independent of the self-inductance and equal to 0.5 or both of s- and d-wave materials. In the strong current regime this exponent depends on the screening. We find $\alpha \approx 1$ for some interval of inductance which agrees with the experimental finding for d-wave ceramic superconductors.