Proximity induced quantum coherence of electrons in multi-terminal
voltage-driven hybrid normal-superconducting nanostructures may result in a
non-trivial interplay between topology-dependent Josephson and Aharonov-Bohm
effects. We elucidate a trade-off between stimulation of the voltage-dependent
Josephson current due to non-equilibrium effects and quantum dephasing of
quasiparticles causing reduction of both Josephson and Aharonov-Bohm currents.
We also predict phase-shifted quantum coherent oscillations of the induced
electrostatic potential as a function of the externally applied magnetic flux.
Our results may be employed for engineering superconducting nanocircuits with
controlled quantum properties
