Resonant amplification of the Andreev process in ballistic Josephson junctions

We study the Josephson effect in ballistic SINIS and SIFIS double-barrier junctions, consisting of superconductors $(S)$, a clean normal $(N)$ or ferromagnetic $(F)$ metal, and insulating interfaces $(I)$. For short SINIS double-tunnel junctions with one channel open for quasiparticle propagation, the critical Josephson current as a function of the junction width shows sharp peaks because of a resonant amplification of the Andreev process: when the quasibound states of the normal interlayer enter the superconducting gap the Andreev bound states are lowered down to the Fermi level. For corresponding SIFIS junctions the quasibound states are spin-split; they amplify the supercurrent less efficiently, and trigger transitions between 0 and $\ensuremath{\pi}$ states of the junction. In contrast to SINIS junctions, a narrow dip related to the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition opens up exactly at the peak due to a compensation of partial currents flowing in opposite directions. With an increased barrier transparency these features are gradually lost, due to the broadening and overlap of quasibound states. Temperature-induced transitions both from 0 to $\ensuremath{\pi}$ and from $\ensuremath{\pi}$ to 0 states are studied by computing the phase diagram (with temperature and junction width as the variables) for different interfacial transparencies varying from metallic to the tunnel limit.