Stationary Josephson effect in a short multiterminal junction

Abstract

We study the dc Josephson effect and the density of states in a multiterminal structure of cross-type geometry that 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 ${\ensuremath{\phi}}_{z}$ between the superconductors in the horizontal wire with a critical current ${I}_{c}$ that can be varied by changing the phase difference ${\ensuremath{\phi}}_{y}$ between the superconductors in the vertical wire. The period of the function ${I}_{Jz}({\ensuremath{\phi}}_{z})$ depends on the ratio of the interface resistances ${R}_{Sn,z}/{R}_{Sn,y}$ being equal to $2\ensuremath{\pi}$ if this ratio is small and equal to $4\ensuremath{\pi}$ in the opposite limit. We also calculate the amplitudes of both the singlet and the odd-frequency triplet components in the system under consideration. The triplet component amplitude may be significantly larger than the amplitude of the singlet component.