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

Abstract

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 δ≪L. 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.

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