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 one-dimensional 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 case, 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 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.

• Received 1 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.174524