# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.05180