Supercurrent quantization in narrow-channel superconductor-normal-metal-superconductor junctions

We study the opening of transport channels in mesoscopic ballistic superconductor-normal-metal superconductor Josephson contacts. Determininig the quasiparticle excitation spectrum in the normal contact region as a function of gate voltage, we discuss the transformation of the electronic levels into phase-sensitive Andreev levels with increasing chemical potential. The opening of these superchannels leads to a supercurrent quantization that exhibits nonuniversal behavior in general, and we discuss its dependence on the junction parameters.