Fraunhofer oscillations of the critical current at a varying Zeeman field in a spin-orbit coupled Josephson junction

TL;DR

This paper investigates how Zeeman fields influence the critical current in spin-orbit coupled Josephson junctions, revealing Fraunhofer-like oscillations dependent on the field orientation and material properties.

Contribution

It demonstrates the emergence of Fraunhofer oscillations in the critical current due to Zeeman field variations in spin-orbit coupled Josephson junctions, comparing Rashba 2D gases and topological insulators.

Findings

Fraunhofer oscillations occur when Zeeman field is perpendicular to contacts.

Oscillation amplitude is larger in topological insulator surface states.

Oscillations are weaker in Rashba spin-orbit coupled 2D gases.

Abstract

The Zeeman interaction results in spontaneous current through a Josephson contact with a spin-orbit coupled normal metal, even in the absence of any voltage, or phase bias. In the case of the Rashba spin orbit coupling of electrons in a two-dimensional (2D) electron gas this effect takes place for the Zeeman field which is parallel to the 2D system and to superconducting contacts. At the same time, the spontaneous current is absent when this field is perpendicular to the contacts. It is shown that in the latter case it may manifest itself in oscillations of the critical Josephson current at the varying Zeeman energy. These oscillations have a form of the Fraunhofer diffraction pattern. The Josephson current under the phase bias was calculated based on the semiclassical Green functions for a disordered 2D electron gas with the strong spin orbit coupling, as well as for surface electrons of a three dimensional topological insulator. In the latter case the diffraction pattern was found to be most pronounced, while in the Rashba gas the oscillations of the critical current are weaker.