A tunable Josephson current in a Rashba Ring by Aharonov-Casher Phase

We study the interference effect induced by the Aharonov-Casher (A-C) phase on the transport between an asymmetrically confined two-dimensional electron ring system and the superconducting leads of a Josephson junction. The Josephson current and the Andreev levels are studied both analytically and numerically. Our results also predict oscillations in the Josephson current due to the A-C phase in the ring that can be tuned electrically via the spin-orbit (SO) interaction. Based on these oscillations, we propose a novel mechanism to observe the A-C phase in mesoscopic rings with gate tunable SO interaction attached to superconducting leads using the Josephson current oscillations. An applicable method to control the Josephson current by a tunable gate voltage can be realized due to these phenomena.