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Coulomb blockade versus coherence in transport through a double junction

We construct a model describing current transport through a superconducting or normal conducting circuit consisting of two point contacts in series by extending a Green’s functions technique. In between the contacts is a mesoscopically large and bulklike island. The model can, in principle, handle contacts in all transmission regimes. Coherent interaction throughout the whole system is included in the form of multiple and multiple Andreev reflections extending over both contacts while accounting for charging effects by a changing electrostatic potential of the island. Our calculations show that even though the onsets of certain current contributions are independent of the island charging energy, Coulomb blockade persists, especially in the normal state. Coulomb staircases can still be visible but get smeared out for particular ratios of the charging energy and the gap in the superconducting state. However, as a general trend, we find that including coherent coupling across the island does not very significantly change the shape of the current-voltage curves compared to the incoherent results.