Switching the sign of Josephson current through Aharonov-Bohm interferometry

The electromagnetostatic Aharonov-Bohm effect is proposed as a tool to realize a fully controllable Josephson pi junction. Both the sign and the magnitude of the supercurrent can be tuned in a ring-shaped ballistic normal region coupled to superconducting electrodes by varying the magnetic flux and the electric field around suitable values. We provide a theoretical description of the system within the scattering matrix theory and discuss its implementation in a realistic setup.