Theory of superconducting proximity effect in a three-dimensional system in the clean limit

The superconducting proximity effect is theoretically investigated for a three-dimensional system in the clean-limit case based on a microscopic wave function. The spatial dependence of the pair potential is clarified with use of the numerical solution of the Gor’kov equation for the step-function S-N model. The reduction of the pair potential at the fixed point of the superconductor side ${\mathrm{\Delta }}_{\mathit{S}}$ is calculated as a measure of the degree of the proximity effect. This quantity is found to be determined by (k${\mathrm{̃}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{F}}$), which is the ratio of the Fermi wave number in the N region to that in the S region. This effect is explained by the conservation of the parallel momentum of the electron to the interface.