Scattering theory of superconductive tunneling in quantum junctions

A consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogolyubov-de Gennes quantum mechanics is presented. The dc Josephson effect and the dc quasiparticle transport in the voltage-biased junctions are considered. Elastic quasiparticle scattering by the junction determines the equilibrium Josephson current. The origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport are discussed. In contrast, quasiparticle tunneling in voltage-biased junctions is determined by inelastic scattering. A general expression for inelastic scattering amplitudes is derived and the quasiparticle current is calculated at all voltages with emphasis on a discussion of the properties of subgap tunnel current and the nature of subharmonic gap structure.