Effect of Finite Reflection at the Interface on Diamagnetic Response of Normal-Superconducting Proximity Contact Double Layers

A quasi-classical theory of diamagnetic response of normal-superconducting proximity contact double layers with a finite reflection at the interface is developed for arbitrary concentrations of impurities. It is found that the reflection at the interface has strong influence on the screening fraction of a system with a finite concentration of impurities, as is the case in the clean limit. Taking into account the finite reflection at the interface, we calculate the temperature dependence of the screening fraction and find good agreement with the recent experimental results obtained for Cu/Ta and Ag/Nb samples.