Destructive interference in transfer rates

Transport through two point-contacts in series, even with arbitrarily high transmissions, can be modeled with rate equations if the rates are deduced from the quantum mechanical current formula, which thus accounts for interferences on the wavefunction level. An expression using Green’s functions giving the current through a single contact is valid for evaluating the charging rates of the enclosed island in the double-junction system, even in the case of coherent coupling all over the island from lead to lead. We demonstrate that these current rates for each junction can be rewritten as 2-products of the so-called transfer Green functions, maintaining formal analogy to the single-junction case. On the one hand this facilitates numerical calculations. On the other hand, the form of the rate terms reveals how besides direct coupling across one junction effective coupling between the involved and the remote lead contributes to transfers across the regarded junction and how coherent loss from the island across the other junction diminishes the rate. It is further explained that for the double junction in the case of coherent coupling between both contacts direct lead-to-lead transport adds current contributions; however, interferences are expected to reduce the net current as compared to incoherent mutual influence via the island charging only. Crossed Andreev reflection in the superconducting state—within the premises of our model—cannot surpass other transport processes such as to cause extra steps in current–voltage curves or negative differential conductance. PACS numbers: 72.10.Bg, 05.60.Gg, 02.90.+p