Finite size effects in metallic superlattice systems

TL;DR

This paper investigates how finite size effects influence the properties of metallic superlattice systems, focusing on the proximity effect and critical temperature, using simple models to compare finite and infinite systems.

Contribution

It introduces a model to analyze finite size effects in metallic superlattices and tests the approximation of constant Cooper pair amplitude across superconducting layers.

Findings

Finite size effects significantly impact the critical temperature.

The constant pair amplitude approximation is valid under certain conditions.

A new model of a single superconducting layer with a realistic pair amplitude is proposed.

Abstract

Clean metallic superlattice systems composed of alternating layers of superconducting and normal materials are considered, particularly aspects of the proximity effect as it affects the critical temperature. A simple model is used to address the question of when a finite--sized system theoretically approximates well a true infinite superlattice. The methods used in the analysis afford some tests of the approximation used that the pair amplitude of the Cooper pairs is constant over a superconducting region. We also use these methods to construct a model of a single superconducting layer which intends to incorporate a more realistic form of the pair amplitude than a simple constant.