Green function techniques in the treatment of quantum transport at the molecular scale

TL;DR

This paper provides a tutorial overview of Green function techniques for modeling quantum charge transport at the molecular scale, emphasizing their application to non-equilibrium and interaction effects.

Contribution

It offers a comprehensive tutorial on applying Green function methods to nanoscale quantum transport, focusing on model Hamiltonian approaches.

Findings

Green function techniques effectively model charge transport at the nanoscale.

Extension to non-equilibrium situations via Keldysh formalism is essential.

Systematic inclusion of interaction effects enhances modeling accuracy.

Abstract

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.