Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

Abstract

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)–voltage () response of the form . Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies and as the percolation threshold of the superconductor is approached from below, where , , and are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear response, i.e., The effective nonlinear response , behaves as , where is the critical exponent of the nonlinear response and is -dependent in general. The results are compared with recently published data, reasonable agreement is found.