Proximity effect and boundary conditions in superconducting-normal double layers

The nucleation fields for superconducting-normal ($s-n$) double layers are calculated for arbitrary thicknesses of the $s$ and $n$ layers when the applied magnetic field is parallel to the $s-n$ interface. One boundary condition was left undetermined in the calculation. Experiments were performed on Pb-Cu and Pb-Sn double layers for various thicknesses of the $s$ and $n$ layers. The boundary condition was extracted by comparing the theoretical and experimental results. It is found that the effective pair potential is approximately continuous across the $s-n$ boundary for a large range of temperatures and all thicknesses of the $s$ and $n$ layers. A simple model is proposed to explain this continuity in terms of an effectively induced pair potential in the $n$ metal near the $s-n$ boundary which is controlled by an electron-phonon interaction different from that in the bulk of the $n$ metal. The nucleation fields of the Pb-Sn double layers as a function of temperature are "$S$-shaped" when Pb is thin, whereas those of Pb-Cu are well behaved. It is proposed that the coherence (extrapolation) length of Sn is magnetic field dependent.