Non-linear conductivity of granular superconductors: A novel breakdown problem

Abstract

The authors study a percolating network of highly hysteretic Josephson junctions in which each junction is modelled as a piecewise ohmic hysteretic device. At the percolation threshold, the average voltage drop across a network on a large L*L grid is assumed to fall to zero as V approximately (I-Ic(L))eta as the applied current is reduced to the critical current Ic(L). The finite-size Monte Carlo study gives the value eta =2.0+or-0.1. This value is remarkably close to the result eta =2 obtained by a scaling analysis of a continuum version of the model.