The BCS critical temperature in a weak external electric field via a linear two-body operator

TL;DR

This paper investigates how a weak external electric field influences the critical temperature of a superconductor using a linearized BCS model, extending previous magnetic field results to electric fields.

Contribution

It introduces a linear approximation approach to analyze the BCS critical temperature under weak electric fields, building on and extending prior magnetic field studies.

Findings

Reproduces known results for magnetic fields in electric field context

Extends linear approximation methods to electric fields

Provides theoretical insights into electric field effects on superconductivity

Abstract

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in [Frank, Hainzl, Seiringer, Solovej, 2016] using the strategy introduced in [Frank, Hainzl, Langmann, 2018], where we considered the case of an external constant magnetic field.