ELECTRIC-FIELD-DEPENDENT VARIABLE-RANGE-HOPPING CONDUCTANCE IN QUASI-2-DIMENSIONAL SYSTEMS - APPLICATION TO PRBA2CU3O7-GAMMA-BASED SUPERCONDUCTOR NORMAL-METAL-SUPERCONDUCTOR JUNCTIONS

We have calculated the hopping conductivity of quasi-two-dimensional s ystems by using the variable-range hopping conduction mechanism in the presence of an electric field. We considered that the localized state s are randomly distributed both in energy and space coordinates. Local ized carriers hop from one state to another in both coordinates. We al so considered that at a particular temperature the localized carriers are distributed according to the Fermi distribution function both belo w and above the Fermi level. The expression of the conductivity for th e constant density of states was calculated. After some approximations , the expression of the conductivity was shown to reduce to expression s found in the literature. We also compared our theory with experiment al results of PrBa2Cu3O7-y based S/N/S junctions. Good agreement betwe en theory and experiment was found.