Quasiparticle current in ballistic constrictions with finite transparencies of interfaces

Nonstationary properties of ballistic constrictions SN/c/NS with disordered NS electrodes are analyzed theoretically. Amplitudes of Andreev and normal reflections at the constriction are related to the solutions of a stationary Green's function problem in an inhomogeneous NS electrode in the dirty limit. This provides a generalization of the model of Octavio, Tinhkam, Blender, and Klapwijk for a spatially inhomogeneous case. The relation between the quasiparticle current in SN/c/NS junctions and the energy spectrum of a NS proximity sandwich is found for arbitrary parameters of N and S materials and of NS interfaces. The effect of the proximity layer on the excess current and the subharmonic structure are analyzed in detail and related to the parameters of the S and N materials. The appearance of series of subharmonic peaks associated with the two-gap structure in the density of states of NS electrodes is demonstrated.