Charge transfer through single molecule contacts: How reliable are rate descriptions?

TL;DR

This paper evaluates the reliability of rate-based descriptions for charge transfer in molecular electronics, demonstrating their surprising accuracy even in regimes where they are expected to fail, through comparison with exact numerical data.

Contribution

It extends the master equation approach to include off-diagonal density matrix elements, improving accuracy in modeling charge-phonon interactions in molecular contacts.

Findings

Rate descriptions are quantitatively accurate even at low temperatures.

Including off-diagonal density matrix elements enhances model accuracy.

Voltage-driven phonon distributions can be approximated by effective thermal states.

Abstract

The trend to fabricate electrical circuits on nanoscale dimensions has led to impressive progress in the field of molecular electronics in the last decade. A theoretical description of molecular contacts as the building blocks of future devices is challenging though as it has to combine properties of Fermi liquids in the leads with charge and phonon degrees of freedom on the molecule. Apart from ab initio schemes for specific set-ups, generic models reveal characteristics of transport processes. Particularly appealing are descriptions based on transfer rates successfully used in other contexts such as mesoscopic physics and intramolecular electron transfer. However, a detailed analysis of this scheme in comparison with numerically exact data is elusive yet. It turns out that a formulation in terms of transfer rates provides a quantitatively accurate description even in domains of parameter space where in a strict sense it is expected to fail, e.g. for lower temperatures. Typically, intramolecular phonons are distributed according to a voltage driven steady state that can only roughly be captured by a thermal distribution with an effective elevated temperature (heating). An extension of a master equation for the charge-phonon complex to include effectively the impact of off-diagonal elements of the reduced density matrix provides very accurate data even for stronger electron-phonon coupling.