Large-N transition temperature for superconducting films in a magnetic field

TL;DR

This paper studies how the critical temperature for superconductivity in thin films depends on film thickness and magnetic field, revealing a minimal thickness needed for superconductivity to occur.

Contribution

It extends the large N Ginzburg-Landau model to include external magnetic fields and confinement, analyzing the critical thickness for superconductivity.

Findings

Existence of a minimal critical thickness for superconductivity.

Superconductivity is suppressed below a certain film thickness.

The behavior depends on the external magnetic field and confinement conditions.

Abstract

We consider the $N$-component Ginzburg-Landau model in the large $N$ limit, the system being embedded in an external constant magnetic field and confined between two parallel planes a distance $L$ apart from one another. On physical grounds, this corresponds to a material in the form of a film in the presence of an external magnetic field. Using techniques from dimensional and $zeta$-function regularization, modified by the external field and the confinement conditions, we investigate the behavior of the system as a function of the film thickness $L$. This behavior suggests the existence of a minimal critical thickness below which superconductivity is suppressed.