Effects of electron-phonon interaction on thermal and electrical transport through molecular nano-conductors

TL;DR

This review discusses how electron-phonon interactions influence charge and heat transport in molecular nano-conductors, introducing multiple theoretical approaches to analyze these effects and their impact on thermoelectric properties.

Contribution

It provides a comprehensive overview of theoretical methods for studying electron-phonon interactions in nano-conductors, including Green's functions, master equations, and Langevin dynamics.

Findings

EPI affects thermoelectric transport properties.

Derived expressions for charge and heat currents under weak EPI.

Demonstrated energy transfer dynamics between electrons and phonons.

Abstract

The topic of this review is the effects of electron-phonon interaction (EPI) on the transport properties of molecular nano-conductors. A nano-conductor connects to two electron leads and two phonon leads, possibly at different temperatures or chemical potentials. The EPI appears only in the nano-conductor. We focus on its effects on charge and energy transport. We introduce three approaches. For weak EPI, we use the nonequilibrium Green's function method to treat it perturbatively. We derive the expressions for the charge and heat currents. For weak system-lead couplings, we use the quantum master equation approach. In both cases, we use a simple single level model to study the effects of EPI on the system's thermoelectric transport properties. It is also interesting to look at the effect of currents on the dynamics of the phonon system. For this, we derive a semi-classical generalized Langevin equation to describe the nano-conductor's atomic dynamics, taking the nonequilibrium electron system, as well as the rest of the atomic degrees of freedom as effective baths. We show simple applications of this approach to the problem of energy transfer between electrons and phonons.