First-order phase transitions in superconducting films: A Euclidean model

TL;DR

This paper models first-order phase transitions in superconducting films using a Euclidean Ginzburg--Landau approach, revealing how the transition temperature varies with film thickness and differs from second-order transitions.

Contribution

It introduces a Euclidean $b4 b4$ model to describe first-order phase transitions in superconducting films and analyzes the dependence of the critical temperature on film thickness.

Findings

Transition temperature $T_c(L)$ is a concave function of film thickness $L$.

The $T_c(L)$ behavior differs significantly from second-order transition models.

Results qualitatively agree with some experimental observations.

Abstract

In the context of the Ginzburg--Landau theory for critical phenomena, we consider the Euclidean $\lambda \phi ^4+\eta \phi^6$ model bounded by two parallel planes, a distance $L$ separating them. This is supposed to describe a sample of a superconducting material undergoing a first-order phase transition. We are able to determine the dependence of the transition temperature $T_{c}$ for the system as a function of $L$. We show that $% T_{c}(L)$ is a concave function of $L$, in qualitative accordance with some experimental results. The form of this function is rather different from the corresponding one for a second-order transition.