Beyond Marcus theory and the Landauer-B\"uttiker approach in molecular junctions: A unified framework

TL;DR

This paper develops a unified theoretical framework that bridges the gap between Marcus theory and the Landauer-Büttiker approach for molecular junction charge transport, addressing their limitations and proposing improved models.

Contribution

It derives a general expression for current in molecular junctions using a quantum master equation, unifying and extending existing theories with practical corrections.

Findings

Marcus theory often fails at low temperatures

Lifetime broadening can be incorporated into Marcus theory

New low-temperature correction improves semi-classical rates

Abstract

Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-B\"uttiker formalism or Marcus theory, respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled to a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression, and present a series of approximations of this result valid at higher temperatures. We find that Marcus theory is often insufficient in describing the molecular charge transport characteristics and gives rise to a number of artefacts, especially at lower temperatures. Alternative expressions, retaining its mathematical simplicity but rectifying those shortcomings, are suggested. In particular, we show how lifetime broadening can be consistently incorporated into Marcus theory, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. Our results are applied to examples building on phenomenological as well as microscopically-motivated electron-vibrational coupling. We expect them to be particularly useful in experimental studies of charge transport through single-molecule junctions as well as self-assembled monolayers.