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

TL;DR

This paper develops a comprehensive non-equilibrium Green's function framework for calculating electron transport in fully interacting nanoscale junctions, ensuring current conservation and addressing inelastic scattering effects.

Contribution

It introduces a generalized Landauer-like current formula for interacting systems with crossing interactions and derives constraints for current conservation in non-equilibrium conditions.

Findings

Derived a current formula with renormalized self-energies.

Showed inelastic scattering terms can be negligible in the thermodynamic limit.

Provided practical Green's function expressions for transport calculations.

Abstract

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.