Critical behavior of nonlinear properties in percolating superconductor/nonlinear-normal conductor networks

Citation
L. Gao et al., Critical behavior of nonlinear properties in percolating superconductor/nonlinear-normal conductor networks, COMM TH PHY, 32(2), 1999, pp. 241-246
Citations number
30
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN THEORETICAL PHYSICS
ISSN journal
02536102 → ACNP
Volume
32
Issue
2
Year of publication
1999
Pages
241 - 246
Database
ISI
SICI code
0253-6102(19990930)32:2<241:CBONPI>2.0.ZU;2-I
Abstract
The critical behavior of nonlinear response in random networks of supercond uctor/nonlinear-normal conductors below the percolation threshold is invest igated. Two cases are examined: (i) The nonlinear normal conductor has weak ly nonlinear current (i)-voltage (v) response of the form v = ri + bi(alpha ) (bi(alpha-1) much less than r and alpha > 1). Both the crossover current density \(J) over right arrow(c)\ and the crossover electric field \(E) ove r right arrow c\ are introduced to mark the transition between the linear a nd nonlinear responses of the network and are found to have power-law depen dencies \(J) over right arrow(c)\ similar to (f(c) - f)(H) and \(E) over ri ght arrow(c)\ similar to (f(c) - f)(M) as the percolation threshold f(c) of the superconductor is approached from below, where H = nu(d) - s(d) > 0, M = nu(d) > 0, nu(d) and s(d) are the correlation-length exponent and the cr itical exponent of linear conductivity in percolating S/N system respective ly; (ii) The nonlinear-normal conductor has strongly nonlinear vi response, i.e., i = chi v(alpha). The effective nonlinear response chi(e) behaves as chi(e) similar to (f(c) - f)(-W(alpha)), where W(alpha) is the critical ex ponent of the nonlinear response chi(e)(alpha) and is alpha-dependent in ge neral. The results are compared with recently published data, reasonable ag reement is found.