Andreev scattering, Josephson-Bloch oscillations and Zener tunneling in heterocontacts of normal and superconductors

The present work covers various aspects of charge transport in heterojunctions consisting of normal conductors (N) and superconductors (S) within the framework of the Bogolyubov-de Gennes-Formalism. The Josephson currents, that are carried by the quasiparticles in the central N layer, are calculated using two different model assumptions: In one case, only scattering states are regarded as initial states, in the other case, while simultaneously taking into account a normal scattering potential, only bound states. The SNS junction is modelled by a superconducting/semiconducting heterostructure, the parameter values of which are geared to the experiments of the group of Herbert Kroemer in Santa Barbara. The alternating Josephson current is calculated in the center of the N layer at temperature T=2.2 K, using the N layer wavefunctions that evolve from the initial states when a voltage V is switched on. The current density shows voltage-dependent current oscillations in time, their period is the inverse of the Josephson frequency