Supercurrents Through Gated Superconductor-Normal-Metal-Superconductor Contacts: the Josephson Transistor

We analyze the transport through a narrow ballistic superconductor-normal-metal-superconductor Josephson contact with non-ideal transmission at the superconductor-normal-metal interfaces, e.g., due to insulating layers, effective mass steps, or band misfits (SIN interfaces). The electronic spectrum in the normal wire is determined through the combination of Andreev- and normal reflection at the SIN interfaces. Strong normal scattering at the SIN interfaces introduces electron- and hole-like resonances in the normal region which show up in the quasi-particle spectrum. These resonances have strong implications for the critical supercurrent I_c which we find to be determined by the lowest quasi-particle level: tuning the potential µ_{x0} to the points where electron- and hole-like resonances cross, we find sharp peaks in I_c, resulting in a transitor effect. We compare the performance of this Resonant Josephson-Transistor (RJT) with that of a Superconducting Single Electron Transistor (SSET).