Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions (Q2890771)

The electron transport properties through fully interacting nanoscale junctions are considered beyond the linear-response regime. The authors calculate the current flow through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green function technique.NEWLINENEWLINEThus, the obtained result for the current equation is general and obtained under only one approximation: there are no direct exchange and correlation effects between the left and right leads. The total current at one of the interfaces (the left one for example) is composed of several terms which can be regrouped into two sets. The first set corresponds to a very generalized Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalized lead self-energies. The second set characterizes inelastic scattering events occurring in the left lead. It is shown how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green functions needed for practical calculations of the current are also provided. Constraints are determined, which are imposed by the physical condition of current conservation.NEWLINENEWLINEThe corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. Its physical interpretation and its relation to previously derived expressions is discussed in detail. Finally, open questions are considered that are of importance for applications of the presented formalism to calculations of quantum transport in realistic systems. These questions concern the location of the interfaces between the central region and the leads, the concept of the extended molecule, the generalized embedding potential, and the calculation of the self-energies.