Charging effects and Andreev reflection in a double-junction circuit: A model approach combining rate equations and Green’s functions

We present a qualitative model for current transport in the superconducting state through a series of two quantum-point contacts with a mesoscopic island between them. A Green's functions technique is merged with a rate-equation method in order to account for phase as well as charging effects. Multiple Andreev reflections are included in a nonperturbative manner and therefore our Ansatz despite some underlying assumptions is in principle not restricted to the low or high transmission regime. We find that in our system, multiple Andreev reflection is not totally suppressed by Coulomb blockade, but that the step pattern of current-voltage characteristics is determined by an interplay of multiple thresholds.