Quantitative simulation of the superconducting proximity effect

Gerd Bergmann

doi:10.1103/PhysRevB.72.134505

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Quantitative simulation of the superconducting proximity effect

Gerd Bergmann

DOI 10.1103/PhysRevB.72.134505 · Physical Review B

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Abstract

A numerical method is developed to calculate the transition temperature of double or multilayers consisting of films of superconductors and normal conductors. The approach is based on a dynamic interpretation of Gorkov’s linear gap equation and is very flexible. The mean free path l of the different metals, transmission through the interface, ratio of specular reflection to diffusive scattering at the surfaces, and fraction of diffusive scattering at the interface can be included. Furthermore, it is possible to vary the mean free path and the BCS interaction NV in the vicinity of the interface. The numerical results show that the normalized initial slope of a superconductor–normal metal (SN) double layer is independent of almost all film parameters except the ratio of the density of states, (ds∕Ts)∣dTc∕ddn∣=Γsn(Nn∕Ns). There are only very few experimental investigations of this initial slope and they consist of Pb∕Nn double layers (Nn stands for a normal metal). Surprisingly the coefficient Γsn in these experiments is of the order or less than 2 while the (weak coupling) theory predicts a value of about 4.5. This discrepancy has not been recognized in the past. The origin of this discrepancy is not understood.