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Superconducting Transition Temperature of Superconducting-Normal Periodic Multi-Layer

Transition temperature T c of superconducting-normal (S-N) periodic multi-layer system is studied in the clean limit. The finite reflection coefficient R at the interface is explicitly taken into account. The obtained gap equation of S-N multi-layer is rather compact and is similar to that of S-N double-layer. The behavior of T c of a periodic multi-layer qualitatively agrees with that of the corresponding double-layer except when the thickness of layer is shorter than the coherence length and R ≃0.5 . Thickness dependence of T c of a periodic multi-layer is in good agreement with the experimental data of Banerjee et al. on the Nb/Cu superlattice.