Control of Josephson current by Aharonov-Casher Phase in a Rashba Ring

TL;DR

This paper investigates how the Aharonov-Casher phase influences the Josephson current in a Rashba spin-orbit coupled ring, revealing oscillations and impurity scattering effects, and proposes a new method for measuring the AC phase.

Contribution

It provides an analytical and numerical study of AC phase-induced Josephson current oscillations in a Rashba ring, including impurity effects and potential for high-sensitivity measurements.

Findings

Josephson current oscillates with the AC phase.

Impurity scattering does not affect oscillations in long channels.

The AC phase can be controlled via gate voltage.

Abstract

We study the interference effect induced by the Aharonov-Casher phase on the Josephson current through a semiconducting ring attached to superconducting leads. Using a 1D model that incorporates spin-orbit coupling in the semiconducting ring, we calculate the Andreev levels analytically and numerically, and predict oscillations of the Josephson current due to the AC phase. This result is valid from the point contact limit to the long channel length limit, as defined by the ratio of the junction length and the BCS healing length. We show in the long channel length limit that the impurity scattering has no effect on the oscillation of the Josephson current, in contrast to the case of conductivity oscillations in a spin-orbit coupled ring system attached to normal leads where impurity scattering reduces the amplitude of oscillations. Our results suggest a new scheme to measure the AC phase with, in principle, higher sensitivity. In addition, this effect allows for control of the Josephson current through the gate voltage tuned AC phase.