Enhanced nonlinear response of superconductor-normal-conductor composite wires and strips

The effective response is calculated in nonlinear composite wires and strips which are modeled as two-dimensional random conductance networks with lateral size L and width δL. We consider a two-component nonlinear conductance network which consists of two types of conductors. The first component is assumed to be nonlinear and obeys a current-voltage (I-V) characteristic of the form I=σ₁V+χ₁V³, while the second component is linear with I=σ₂V, where σ₁ and σ₂ are the linear conductances and χ₁ is the nonlinear conductance. We invoke a renormalization-group (RG) analysis to rescale the strip repeatedly by small-cell transformations to obtain a chain of nonlinear conductors, for which exact formulas of the effective linear response σₑ and nonlinear response χₑ are available. We calculate σₑ and χₑ as a function of the volume fraction for various conductance ratios and examine the dependence on δ. We observe large enhancements in the nonlinear response under appropriate conditions, as well as interesting crossover from one- to two-dimensional behaviors as δ increases. Numerical simulations are performed to verify the RG calculations. Scaling exponents are determined in the RG and compared with available estimates; good agreements are found. Possible generalizations of the present investigation are discussed.