Boundary conditions for the order parameter and the proximity influenced internal phase differences in double superconducting junctions

TL;DR

This paper explores how boundary conditions influence internal phase differences in double superconducting junctions, revealing complex behaviors that affect current-phase relations and are analyzed via the Ginzburg-Landau approach.

Contribution

It derives boundary conditions for the superconductor order parameter in double junctions within the Ginzburg-Landau theory and analyzes their impact on phase difference behaviors.

Findings

Internal phase differences do not have a one-to-one correspondence with external phase difference.

The range of internal phase differences is reduced, preventing 4π-periodic current-phase relations.

Supercurrent-induced phase incursion and mode interchanging are significant effects in SINIS and SISIS junctions.

Abstract

This paper gives an overview of the unconventional dependence of internal phase differences on the external phase difference in superconductor-normal metal-superconductor (SINIS) and superconductor-superconductor-superconductor (SISIS) tunnel double junctions. The results are obtained within the Ginzburg-Landau (GL) approach that includes boundary conditions for the superconductor order parameter in the presence of a Josephson coupling through interfaces. The boundary conditions are derived within the GL theory and substantiated microscopically. The absence of the one-to-one correspondence between external $\phi$ and internal $\chi_{1,2}$ phase differences in the junctions is shown to occur in two qualitatively different ways, both of which result in the range of $\chi_{1,2}$ reduced and prevent the $4\pi$-periodic current-phase relation $j=j_c\sin\frac{\phi}{2}$. In SINIS junctions, the effect of the supercurrent-induced phase incursion $\varphi$ between the end faces of the central electrode of mesoscopic length $L$ can play a crucial role. In SISIS junctions, there occurs the regime of interchanging modes, which is modified as $L$ decreases. The proximity and pair breaking effects in the double junctions with closely spaced interfaces are addressed.