Long-range Josephson effect in mesoscopic T-shaped superconductor–normal-metal–superconductor junctions

It is found that the dc Josephson current in a ballistic superconductor--normal-metal--superconductor junction connected to an electron reservoir does not decay with the length of the junction if voltage is applied between the reservoir and the junction. At finite temperature, this nonequilibrium Josephson current is proportional to the applied voltage and saturates at eV>Δ at a level typical for the critical current of short junctions. In asymmetric junctions the current-phase dependence is {π} periodic.