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
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.