Non-equilibrium quantum transport in fully interacting single-molecule nanojunctions

TL;DR

This paper develops a comprehensive theoretical framework using non-equilibrium Green's functions to accurately calculate electron transport in fully interacting nanojunctions, including complex interactions at contacts and within leads.

Contribution

It introduces a generalized current formula accounting for interactions throughout the system, extending previous models to include inelastic scattering and crossing interactions beyond mean-field approximations.

Findings

Derivation of a generalized Meir-Wingreen current expression.

Inclusion of inelastic scattering effects in leads.

Framework for practical calculations using generalized embedding potentials.

Abstract

Using non-equilibrium Green's functions, we derive a formula for the electron current through a lead-molecule-lead nanojunction where the interactions are not restricted to the central region, but are spread throughout the system, including the leads and the lead-molecule interfaces. The current expression consists of two sets of terms. The first set corresponds to a generalised Meir and Wingreen expression where the leads' self-energies are renormalised by the interactions crossing at the molecule-lead contacts. The second set corresponds to inelastic scattering events in the leads arising from any arbitrary interaction, including electron-electron and electron-phonon coupling, treated beyond mean-field approximations. Using different levels of approximation, we are able to recover well-known expressions for the current. We also analyse how practical calculations can be performed with our formalism by using the new concept of generalised embedding potentials.