GAO Lei, JIANG Qing, LI ZhenYa
理论物理通讯. 1999, 32(2): 241-246.
The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi
α (bi
α-1《t and α > 1). Both the crossover current density

and the crossover electric field

are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies

~(f
c - f)
H and

~(f
c - f)
M as the percolation threshold f
c of the superconductor is approached from below, where
H = ν
d - s
d > 0, M = ν
d > 0, ν
d and s
d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X
να The effective nonlinear response X
e, behaves as X
e ~(f
c - f)
-W(α), where W ( α ) is the critical exponent of the nonlinear response x
e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.