Quantum interference in a Cooper pair splitter: The three sites model

New generation of Cooper pair splitters defined on hybrid nanostructures are devices with high tunable coupling parameters. Transport measurements through these devices revealed clear signatures of interference effects and motivated us to introduce a new model, called the 3-sites model. These devices provide an ideal playground to tune the Cooper pair splitting (CPS) efficency on demand, and displays a rich variety of physical phenomena. In the present work we analyze theoretically the conductance of the 3-sites model in the linear and non-linear regimes and characterize the most representative features that arise by the interplay of the different model parameters. In the linear regime we find that the local processes typically exhibit Fano-shape resonances, while the CPS contribution exhibits Lorentzian-shapes. Remarkably, we find that under certain conditions, the transport is blocked by the presence of a dark state. In the non-linear regime we established a hierarchy of the model parameters to obtain the conditions for optimal efficency.