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

TL;DR

This study models disordered granular superconductors with Josephson junctions to analyze their nonlinear ac resistivity, revealing that the resistivity's power-law behavior depends on inductance and current regime, with findings aligning with experimental data.

Contribution

It introduces a detailed dynamical model for s-wave and d-wave disordered granular superconductors, highlighting the non-universality of the nonlinear resistivity exponent and its dependence on physical parameters.

Findings

Exponent $oldsymbol{eta}$ varies with inductance and current regime.

In weak currents, $oldsymbol{eta}$ is approximately 0.5 for both s- and d-wave.

In strong currents, $oldsymbol{eta}$ approaches 1, matching experimental results.

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.