Modelling partially coherent transport across an island - multiple Andreev reflection and charging effects

Abstract

A Green's functions technique known to describe transport through a superconducting point contact with multiple Andreev reflection is merged with a rate equation scheme and thus extended to model transport through a series of two junctions enclosing an island between them. In the superconducting state such systems may show an interplay of multiple Andreev reflection and Coulomb blockade. Although not of unique shape calculated current-voltage characteristics exhibit more or less pronounced steps that can be associated to transport processes setting in because of the applied voltage becoming sufficient to overcome certain fractions of the superconductor gap or providing the required charging energy. The speciality of our model, however, lies in regarding all single-charge transfers out of every-order multiple reflection simultaneously instead of adding total rates for processes up to some order. The algorithm can treat series of junctions that are just incoherently coupled via the electrostatic charge on the island as well as transport maintaining coherence across the island. In the latter case we find direct lead-to-lead transport, but interestingly, Coulomb blockade never completely vanishes in our model. In principle, the scheme is also applicable to a mixed situation where interaction between the junctions is partly coherent and partly incoherent.