# Resonant inelastic tunneling in molecular junctions

**Authors:** Michael Galperin, Abraham Nitzan, Mark A. Ratner  
**arXiv:** [cond-mat/0510452](https://arxiv.org/abs/cond-mat/0510452)  
**Date:** 2005-10-17  
**Summary page:** https://www.summarizepaper.com/en/paper/cond-mat--0510452v2/

## Key points

- Self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction
- Phonon-assisted resonance level model that considers mutual influence of electron and phonon subsystems
- Second-order cumulant expansion used to express correlation function of phonon shift generator in terms of phonon momentum Green function
- Equation of motion (EOM) method used to obtain approximate analog of Dyson equation for electron and phonon Green functions
- Emphasis on importance of self-consistency in resonance tunneling situations, especially with partially filled bridge levels
- Confirmation of absence of phonon sidebands in current vs. gate voltage plots at small source-drain voltage, even for systems with strong vibronic coupling
- Comprehensive framework for understanding electron transport in molecular junctions with significant electron-phonon interaction
- Insights into how these interactions influence transport properties and can be applied to various experimental setups involving molecular electronics
- Essential self-consistent procedure for accurately predicting transport behavior under different conditions and exploring phenomena related to vibronic coupling in molecular electronics devices.

## Summary

In this study, the authors present a self-consistent procedure for calculating electron transport currents in molecular junctions with intermediate to strong electron-phonon interaction. They develop a phonon-assisted resonance level model that takes into account the mutual influence of the electron and phonon subsystems. The model is based on a second-order cumulant expansion, which allows them to express the correlation function of the phonon shift generator in terms of the phonon momentum Green function. They also use the equation of motion (EOM) method to obtain an approximate analog of the Dyson equation for the electron and phonon Green functions, considering many-particle operators present in the Hamiltonian. The authors emphasize the importance of self-consistency in resonance tunneling situations, particularly when dealing with partially filled bridge levels. They stress that their approach differs from previous ones by considering this self-consistency aspect. Through their calculations, they confirm a previous suggestion regarding the absence of phonon sidebands in current vs. gate voltage plots when the source-drain voltage is small, even for systems with strong vibronic coupling. Overall, this study provides a comprehensive framework for understanding electron transport in molecular junctions with significant electron-phonon interaction. It offers valuable insights into how these interactions influence transport properties and can be applied to various experimental setups involving molecular electronics. The self-consistent procedure developed here is essential for accurately predicting transport behavior under different conditions and can be used to further explore phenomena related to vibronic coupling in molecular electronics devices.