Proximity effect in multiterminal hybrid structures

TL;DR

This paper investigates how the superconducting order parameter in multiterminal ferromagnet-superconductor structures is affected by the magnetic alignment and the transparency of additional electrodes, revealing complex proximity effects and oscillations.

Contribution

It provides a detailed analysis of the proximity effect in multiterminal FSF structures, highlighting how multiple ferromagnetic electrodes influence the superconducting order parameter and local density of states.

Findings

Superconducting order parameter is larger in ferromagnetic alignment than in antiferromagnetic.

Adding a third electrode can reverse the order parameter difference depending on transparency.

Friedel oscillations occur in the Gorkov function with finite electrode separation.

Abstract

We consider the proximity effect in multiterminal ferromagnet superconductor (FSF) hybrid structures in which two or three electrodes are connected to a superconductor. We show that two competing effects take place in these systems: (i) pair breaking effects due to the response to the exchange field induced in the superconductor; (ii) a reduction of the \SOP at the interface that takes place already in NS junctions. We focus on this second effect that dominates if the thickness of the S layer is small enough. We consider several single-channel electrodes connected to the same site. We calculate the superconducting order parameter and the local density of state (LDOS). With two ferromagnetic electrodes connected to a superconductor we find that the superconducting order parameter in the ferromagnetic alignment is larger than the superconducting order parameter in the antiferromagnetic alignment ($\Delta_{\rm F} >\Delta_{\rm AF}$), in agreement with [Eur. Phys. J. B {\bf 25}, 373 (2002)]. If a third spin polarized electrode is connected to a superconductor we find that $\Delta_{\rm F}-\Delta_{\rm AF}$ can change sign as the transparency of the third electrode increases. This can be understood from the fact that the superconducting order parameter is reduced if pair correlations among the ferromagnetic electrodes increase. If the two ferromagnetic electrodes are within a finite distance we find Friedel oscillations in the Gorkov function but we still obtain $\Delta_{\rm F} > \Delta_{\rm AF}$.