Stationary Josephson effect in a short multi-terminal junction

TL;DR

This paper investigates the dc Josephson effect in a four-terminal superconducting structure with a cross geometry, revealing how the critical current depends on phase differences and interface resistances, and analyzing singlet and triplet components.

Contribution

It provides a detailed analysis of the phase-dependent Josephson current and density of states in a multiterminal junction, including the influence of interface resistances and the behavior of singlet and triplet components.

Findings

Josephson current exhibits sinusoidal dependence on phase difference.

Critical current can be tuned by phase difference in the perpendicular wire.

Triplet component amplitude can surpass singlet component amplitude.

Abstract

We study the dc Josephson effect and the density of states in a multiterminal structure of cross-type geometry which consists of four superconducting electrodes connected by one-dimensional normal or ferromagnetic wires. We find that the Josephson current $I_{Jz}$ has a sinusoidal dependence on the phase difference $\phi_z$ between the superconductors in the horizontal wire with a critical current $I_c$ that can be varied by changing the phase difference $\phi_y$ between the superconductors in the vertical wire. The period of the function $I_{Jz}(\phi_z)$ depends on the ratio of the interface resistances $R_{Sn,z}/R_{Sn,y}$ being equal to $2\pi $ if this ratio is small and equal to $4\pi $ in the opposite limit. We also calculate the amplitudes of both the singlet and the odd-frequency triplet component in the system under consideration. The triplet component amplitude may be significantly larger than the amplitude of the singlet component.