Resonant inelastic tunneling in molecular junctions

TL;DR

This paper presents a self-consistent theoretical framework for calculating electron transport in molecular junctions with strong electron-phonon interactions, emphasizing the importance of mutual subsystem influence and confirming the absence of phonon sidebands under certain conditions.

Contribution

It introduces a novel self-consistent method combining cumulant expansion and equation of motion techniques for modeling resonant tunneling with strong vibronic coupling.

Findings

Self-consistent approach captures electron-phonon mutual influence.

Confirms absence of phonon sidebands at low source-drain voltage.

Applicable to intermediate and strong electron-phonon coupling regimes.

Abstract

Within a phonon-assisted resonance level model we develop a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. The scheme takes into account the mutual influence of the electron and phonon subsystems. It is based on the 2nd order cumulant expansion, used to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. Equation of motion (EOM) method is used to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions in the case of many-particle operators present in the Hamiltonian. To zero-order it is similar in particular cases (empty or filled bridge level) to approaches proposed earlier. The importance of self-consistency in resonance tunneling situations (partially filled bridge level) is stressed. We confirm, even for strong vibronic coupling, a previous suggestion concerning the absence of phonon sidebands in the current vs. gate voltage plot when the source-drain voltage is small.