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

TL;DR

This paper presents a self-consistent field approach to study the proximity effect in normal metal-superconductor structures, revealing smaller induced gaps and aligning qualitatively with experimental spectral densities.

Contribution

It introduces a new self-consistent method based on diagrammatic perturbation theory to analyze the proximity effect, differing from traditional theories by predicting smaller induced gaps.

Findings

Induced energy gaps in normal metals are smaller than those predicted by traditional theories.

The frequency dependence of spectral density matches experimental observations.

The method simplifies calculations of Green's functions in superconductor-normal metal systems.

Abstract

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.