Quantitative Simulation of the Superconducting Proximity Effect

TL;DR

This paper introduces a flexible numerical method to calculate the transition temperature in superconductor-normal metal multilayers, revealing discrepancies with weak coupling theory and suggesting strong coupling effects in experiments.

Contribution

It develops a dynamic interpretation of Gorkov's gap equation for multilayers, accounting for various interface and film parameters, and explains experimental deviations through strong coupling effects.

Findings

Normalized initial slope is mostly independent of film parameters.

Experimental initial slopes are lower than weak coupling predictions.

Strong coupling effects explain the experimental results.

Abstract

A numerical method is developed to calculate the transition temperature of double or multi-layers consisting of films of super- 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 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 an SN double layer is independent of almost all film parameters except the ratio of the density of states. 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 of the initial slope 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 autor suggests that it is due to strong coupling behavior of Pb in the double layers. The strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for the coefficient. This agrees much better with the few experimental results that are available. PACS: 74.45.+r, 74.62.-c, 74.20.Fg