Rediscovery of Cooper pair factor

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.