The external field dependence of the BCS critical temperature

TL;DR

This paper investigates how weak external fields affect the critical temperature in BCS theory, revealing that in a certain limit, the critical temperature's correction is governed by the lowest eigenvalue of a linearized Ginzburg-Landau operator.

Contribution

It provides a rigorous analysis linking the external field dependence of the BCS critical temperature to the spectral properties of the linearized Ginzburg-Landau equation.

Findings

The next-to-leading order of the critical temperature is determined by the lowest eigenvalue.

External fields influence the critical temperature through spectral properties.

The analysis applies in the limit of microscopic to macroscopic scale ratio tending to zero.

Abstract

We consider the Bardeen-Cooper-Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg-Landau equation.