Superconducting transition temperature in thin films

TL;DR

This paper uses a modified Ginzburg-Landau model and Matsubara formalism to analytically derive how the superconducting transition temperature decreases linearly with inverse film thickness, matching experimental observations.

Contribution

It provides a theoretical derivation of the dependence of T_c on film thickness using a modified Ginzburg-Landau approach and identifies the critical thickness for superconductivity suppression.

Findings

T_c decreases linearly with inverse thickness

Critical thickness for superconductivity suppression is derived

Model matches experimental trends

Abstract

By considering the Ginzburg-Landau model, compactified in one of the spatial dimensions, and using a modified Matsubara formalism, we determine the dependence of the superconducting transition temperature (T_c) of a film as a function of its thickness (L). We show that T_c is a decreasing linear function of L^{-1}, as has been found experimentally. The critical thickness for the suppression of superconductivity is expressed in terms of the Ginzburg-Landau parameters.