Current-voltage characteristics of diluted Josephson-junction arrays: scaling behavior at current and percolation threshold

TL;DR

This study investigates the current-voltage characteristics of diluted Josephson-junction arrays, revealing power-law behavior above the percolation threshold and scaling near the superconducting transition at the percolation threshold.

Contribution

It provides a detailed analysis of the scaling behavior of IV characteristics in disordered Josephson arrays at and near the percolation threshold, including finite temperature effects.

Findings

Power-law IV behavior above p_c with disorder-dependent critical current

Scaling behavior consistent with a simple scaling analysis

Linear resistance vanishes as temperature decreases, with crossover currents related to T^{1+ν_T}

Abstract

Dynamical simulations and scaling arguments are used to study the current-voltage (IV) characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where $p_c$ is the percolation threshold. For $p$ $>$ $p_c$ and zero temperature, the IV curves show power-law behavior above a disorder dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At $p_c$ and finite temperature $T$, the results show the scaling behavior of a T=0 superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to non-linearity appears at currents proportional to $% T^{1+\nu_T}$, with a thermal-correlation length exponent $\nu_T$ consistent with the corresponding value for the diluted XY model at $p_c$.