Superconductive properties of thin dirty superconductor-normal-metal bilayers

The theory of superconductivity in thin superconductor-normal-metal (SN) sandwiches (bilayers) in the diffusive limit is developed within the standard Usadel equation method, with particular emphasis on the case of very thin superconductive layers, d(s)<<d(N). The proximity effect in the system is governed by the interlayer interface resistance (per channel) rho (int). The case of relatively low resistance (which can still have large absolute values) can be completely studied analytically. The theory describing the bilayer in this limit is of BCS type but with the minigap (in the single-particle density of states) E-g<<Delta substituting the order parameter Delta in the standard BCS relations; the original relations are thus severely violated. In the opposite limit of an opaque interface, the behavior of the system is in many respects close to the BCS predictions. Over the entire range of rho (int), the properties of the bilayer are found numerically. Finally, it is shown that the results obtained for the bilayer also apply to more complicated structures such as SNS and NSN trilayers, SNINS and NSISN systems, and SN superlattices.