Superconducting transition temperature of proximity-contact superconducting-normal double layers

The transition temperature of a proximity-contact superconducting-normal finite double layer is discussed in the clean limit. The finite reflection coefficient R at the interface is explicitly taken into account. The thickness dependence and the R dependence of ${\mathit{T}}_{\mathit{c}}$ are discussed. It is shown that the transition temperature of a very thin double layer cannot be well described by Cooper’s formula. The present results qualitatively agree with experiments.