Enhancement in nonlinear effects in percolating nonlinear resistor networks

The nonlinear response is studied in a percolating network of superconductor and normal conductor with nonlinear I-V characteristic below the percolation threshold of the superconductor. The crossover current density $J_{\mathrm{L}\mathrm{-}\mathrm{NL}}$, defined as the current density at which the linear and nonlinear responses of the network become comparable, is found to have a power-law dependence $J_{\mathrm{L}\mathrm{-}\mathrm{NL}\mathrm{\sim }(p_c\mathrm{-}\mathrm{p}{)}^H}$ as the percolation threshold is approached from below. With use of a model of the percolating network below $p_c$ analogous to the nodes-links-blobs picture, H is found to be H=${\nu }_d$(d-1)-1, where ${\nu }_d$ is the correlation-length exponent and d is the dimensionality of the lattice.