Crossover exponents in percolating superconductor{endash}nonlinear-conductor mixtures
- Chinese Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing, 100080, Peoples Republic of (China)
The nonlinear response is studied in a two-component composite with concentration {ital p} of superconductor (S) and concentration 1{minus}{ital p} of normal conductor (N) with nonlinear response of the form {ital J}={sigma}{sub 1}{ital E}+{chi}{sub 1}{ital E}{sup {beta}} ({beta}{approx_gt}1). Below the percolation threshold {ital p}{sub {ital c}} of the superconductor, the response of the composite can be represented by {l_angle}{ital J}{r_angle}={sigma}{sub {ital eE}}+{chi}{sub {ital eE}}{sup {beta}}, where {l_angle}...{r_angle} represents spatial averages. The magnitude of the crossover field {ital E}{sub {ital c}}, defined as the electric field at which the linear and nonlinear response of the composite become comparable, is found to have a power-law dependence {ital E}{sub {ital c}}{approximately}({ital p}{sub {ital c}}{minus}{ital p}){sup M({beta})}, and the corresponding crossover current {ital I}{sub {ital c}} is found to have similar dependence {ital E}{sub {ital c}}{approximately}({ital p}{sub {ital c}}{minus}{ital p}){sup W({beta})} as the percolation threshold is approached from below. By using a connection between the nonlinear response of the random nonlinear composite problem and the conductance fluctuation of the corresponding random linear composite problem the explicit expressions for M({beta}) and W({beta}) are calculated. We prove that both M({beta}) and W({beta}) are monotonically decreasing functions of {beta}, which have the special values M(1{sup +})=W(1{sup +})=+{infinity}, M(3)=[{kappa}{prime}(2)+{ital s}/2], W(3)=[{kappa}{prime}(2){minus}{ital s}/2], M(+{infinity})=(2{minus}{ital d}){nu}/2{le}0, W(+{infinity})={minus}({ital s}+{zeta}{sub {ital G}})/2{lt}0. The magnitude of the crossover field {ital E}{sub {ital c}} and the corresponding crossover current {ital I}{sub {ital c}} are discussed as functions of {beta} and some interesting crossover effects are reported. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 459843
- Journal Information:
- Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 1 Vol. 53; ISSN 0163-1829; ISSN PRBMDO
- Country of Publication:
- United States
- Language:
- English
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