Proximity effect and self-consistent field in a normal metal-superconductor structure

The concept of a self-consistent field in the theory of superconductivity based on the diagram method of the time-dependent perturbation theory is presented. It is shown that the well-known Bardeen-Cooper-Schrieffer equation for the order parameter of superconductivity is already realized in a zero approximation.The form of interaction Hamiltonian uniquely determines a chain of interconnected Green's functions which are easily calculated in this approximation. On the basis of the presented method a proximity effect in a normal metal-superconductor structure is studied. It was obtained the energy gap values induced in a normal metal. In contrast to the traditional McMillan and de Gennes theories with self-consistent Green's functions the self-consistency over the order parameter gives a significantly smaller gap value induced in a normal metal. The frequency dependence of the homogeneous spectral density is obtained which qualitatively agrees with experiment.