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 ${\mathit{I}}_{\mathit{c}}$ through such a system as a function of the gate voltage ${\mathit{V}}_{\mathit{g}}$ taking into account parity effects in the superconductors. The dependence ${\mathit{I}}_{\mathit{c}}$(${\mathit{V}}_{\mathit{g}}$) shows resonant singularities and has a qualitatively different character for Δ<${\mathit{E}}_{\mathit{C}}$ and Δ>${\mathit{E}}_{\mathit{C}}$, Δ being the superconducting gap and ${\mathit{E}}_{\mathit{C}}$=${\mathit{e}}^2$/2C 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.