Andreev-level tunneling in a ballistic double superconductor normal-metal-superconductor junction

The supercurrent in a mesoscopic, ballistic, and symmetrically stacked, double superconductor-normal-metal-superconductor (SNS) junction is studied. Our focus is to establish the features in the supercurrent that are associated with the Andreev-level tunneling between the two SNS junctions. Both the junction geometry dependence and the gap function dependence are studied and are analyzed in terms of the quasiparticle scattering processes. The quasiparticle scattering is worked out analytically by solving the Bogoliubov-de Gennes equation within the Andreev approximation. The current is calculated, following Beenakker and van Houten [Phys. Rev. Lett. 66, 3056 (1991)], and the result is found to differ from that of the transmission approach. Such discrepancy between the two approaches, however, is found to disappear for a single SNS junction. In our result, the currents in the two normal regions are checked to be the same.