Hopping conduction in insulator-conductor-superconductor mixtures

Abstract

The coherent medium approximation is applied to study the frequency-dependent diffusion constant in two- and three-dimensional ant-termite like mixtures, where three types of jump rates, 'normal' (metallic), 'superconducting' and 'insulating' are distributed randomly. The DC diffusion constant vanishes when (p+r)<or=pc and is proportional to (p+r-pc)/(rc-r) when p+r>pc, where p and r are the probabilities that a given bond is metallic and superconducting, respectively, and z is the coordination number of the lattice, pc=rc identical to 2/z. In the low-frequency limit, the real and imaginary parts of the AC diffusion constant go as A(z,d,p,r)f( omega ) and B(z,d,p,r)g( omega ), respectively, a behaviour similar to the pure ant limit. The behaviour of f( omega ) and g( omega ) is examined below, at and above the percolation thresholds, in both two and three dimensions. The coefficients A and B of these leading terms diverge as r to rc (superconducting region percolates), indicating enhancement in the dielectric constant.