A minimal size for granular superconductors

TL;DR

This paper explores the smallest possible size of superconducting grains using a Ginzburg-Landau model confined to a spherical geometry, deriving a critical radius below which superconductivity cannot occur.

Contribution

It introduces a theoretical framework to determine the minimal size of superconducting grains based on their transition temperature and geometry.

Findings

Derived an equation for critical temperature as a function of grain size

Identified a minimal radius for superconductivity in spherical grains

Provided insights into size effects on superconducting transition

Abstract

We investigate the minimal size of small superconducting grains by means of a Ginzburg-Landau model confined to a sphere of radius $R$. This model is supposed to describe a material in the form of a ball, whose transition temperature when presented in bulk form, $T_{0}$, is known. We obtain an equation for the critical temperature as a function of $R$ and of $T_{0}$, allowing us to arrive at the minimal radius of the sphere below which no superconducting transition exists.