Note on possibility of proximity induced spontaneous currents in superconductor/normal metal heterostructures

TL;DR

This paper investigates whether spontaneous currents can arise in superconductor/normal metal heterostructures due to the proximity effect, analyzing free energy contributions and stability of current-carrying states.

Contribution

It provides a theoretical analysis of free energy components showing that spontaneous currents are energetically unfavorable in S/N heterostructures.

Findings

Proximity effect increases the free energy of the normal metal film.

Boundary terms decrease the total free energy.

Current-carrying states are energetically unfavorable.

Abstract

We analyse the possibility of the appearance of spontaneous currents in proximated superconducting/normal metal (S/N) heterostructure when Cooper pairs penetrate into the normal metal from the superconductor. In particular, we calculate the free energy of the S/N structure. We show that whereas the free energy of the N film $F_{N}$ in the presence of the proximity effect increases compared to the normal state, the total free energy, which includes the boundary term $F_{B}$, decreases. The condensate current decreases $F_{N}$, but increases the total free energy making the current-carrying state of the S/N system energetically unfavorable.