1202.3393 (H. Ness et al.)

Many-body current formula and current conservation for non-equilibrium
fully interacting nanojunctions    [PDF]

H. Ness, L. K. Dash

We consider the electron transport properties through fully interacting
nanoscale junctions beyond the linear-response regime. We calculate the current
flowing through an interacting region connected to two interacting leads, with
interaction crossing at the left and right contacts, by using a non-equilibrium
Green's functions (NEGF) technique. The total current at one interface (the
left one for example) is made of several terms which can be regrouped into two
sets. The first set corresponds to a very generalised Landauer-like current
formula with physical quantities defined only in the interacting central region
and with renormalised lead self-energies. The second set characterises
inelastic scattering events occurring in the left lead. We show 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's functions needed for practical calculations of the current
are also provided. We determine the constraints imposed by the physical
condition of current conservation. The corresponding equation imposed on the
different self-energy quantities arising from the current conservation is
derived. We discuss in detail its physical interpretation and its relation with
previously derived expressions. Finally several important key features are
discussed in relation to the implementation of our formalism for calculations
of quantum transport in realistic systems.

View original: http://arxiv.org/abs/1202.3393