Rediscovery of Cooper pair factor

TL;DR

This paper explores the universal nature of the Cooper pair factor in superconductivity and proposes a supersymmetric explanation for the phase factor in the Aharonov-Bohm effect, extending to nonlinear sigma models coupled with supergravity.

Contribution

It introduces a supersymmetric model that explains the Cooper pair factor without relying on electron pairing arguments, linking superconductivity and topological effects.

Findings

The Cooper pair factor is shown to be universal.

A supersymmetric model reproduces the phase factor in the AB effect.

Application to nonlinear sigma models coupled with supergravity.

Abstract

In superconductivity, the Cooper pair \cite{Ref1} is a bound state of a pair of weakly interacting electrons in a metal which forces us to insert a factor of $2e$ (instead of $e$) in the phase of the wave function in the Aharonov-Bohm (AB) effect. We claim that the existence of such a factor is universal. In \cite{Ref2}, we proposed an explanation for the AB effect (or equivalently, a supersymmetric Dirac monopole) based on SUSY. It is shown that this model opens a path to recapture this factor without the need for arguments related to attractive pairs. The idea is also applied to the case of a nonlinear sigma model (NLSM) when it is coupled to $\mathcal{N}=1$, supergravity.