Josephson effect in low-capacitance superconductor--normal-metal--superconductor systems

The transport properties of a small superconductor--normal-metal--superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current [ital I][sub [ital c]] through such a system as a function of the gate voltage [ital V][sub [ital g]] taking into account parity effects in the superconductors. The dependence [ital I][sub [ital c]]([ital V][sub [ital g]]) shows resonant singularities and has a qualitatively different character for [Delta][lt][ital E][sub [ital C]] and [Delta][gt][ital E][sub [ital C]], [Delta] being the superconducting gap and [ital E][sub [ital C]]=[ital e][sup 2]/2[ital C] being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.