Temperature and electric field dependent variable range hopping conduction in high temperature superconductor S/N/S junctions

We have calculated the temperature and electric field dependent variable range hopping conductivity of quasi-two dimensional systems. We considered the effect of the electron-electron interaction through the density of states in the variable range hopping mechanism. In the presence of the electron-electron interaction, the density of states is proportion to the energy of the localized electrons. Using this density of states, the expressions of the conductivity are calculated by using the method developed in reference [6]. At zero electric field, our results for temperature dependent of conductivity reduces to that of given in the literature. We found that for beta much greater than 1, the logarithm of conductivity is proportional to beta(-1/3) for the constant density of states and to beta(-1/2) in the presence of electron-electron interactions. Here beta is proportional to an electric field and inversely proportional to the temperature. The present theory is used to explain the electric and temperature dependent conductivity data of PrBa2Cu3O7-y thin films and PrBa2Cu3O7-y based S/N/S junctions. A good agreement between theory and experiment has been found.