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Title: Anomalous transport in random superconducting composite systems
Authors: Yu, KW
Issue Date: 15-May-1989
Source: Journal of applied physics, 15 May 1989, v. 65, no. 10, p. 3747-3755
Abstract: We have studied anomalous diffusion in the random superconducting network (RSN) with a wide distribution of conductivity. We consider a composite medium of superconducting and normal conducting regions in which the normal conducting component obeys a transfer-rate distribution of the form W ⁻⁽¹⁺ᵅ⁾(0<α<1). In the static (dc) case below the percolation threshold P[sub c], one finds that the dc conductivity varies as (P[sub c]- p)[sup -s'] in the vicinity of P[sub c] with s' = l/α. Above the percolation threshold and in the RSN limit, the superconducting component is considered to possess a large but finite transfer rate W[sub s]. In this limit, the dc conductivity follows the P=P[sub c] behavior for small W[sub s], crossing over to the behavior of ordinary percolation at a crossover value of the superconducting transfer rate W[sub s,co], which is found to vary as (p-p[sub c])⁻⁽¹⁺ᵅ ⁾/ᵅ. The results are in good accord with scaling relations. Right at the percolation threshold, the frequency-dependent conductivity is calculated in the RSN limit. The real part of the conductivity (α[sub R] at low frequencies initially follows the dc behavior, crossing over to the behavior α[sub R]~w¹ ⁻ᵅ at high frequencies. The crossover frequencies are estimated for various relevant regions. The imaginary part of the conductivity (σ₁) has even more complex behaviors. At high frequencies, σ₁varies as W¹ ⁻ᵅ, being the same as the real part. The results are in accord with the scaling relations generalized to finite frequencies. The model is also numerically solved in the effective medium approximation to compare with the analytic results. Good agreements are found.
Keywords: Anomalous properties
Percolation theory
Random walk
Superconducting composites
Scaling laws
Network analysis
Electric conductivity
Publisher: American Institute of Physics
Journal: Journal of applied physics 
ISSN: 0021-8979
EISSN: 1089-7550
DOI: 10.1063/1.343384
Rights: © 1989 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in K. W. Yu, J. Appl. Phys. 65, 3747 (1989) and may be found at
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