Beyond Marcus theory and the Landauer-Buttiker approach in molecular junctions. II. A self-consistent Born approach

TL;DR

This paper introduces a self-consistent Born approximation method for modeling charge transport in molecular junctions, improving accuracy over previous theories especially under strong electron-vibrational coupling, and unifies Marcus and Landauer-Buttiker approaches.

Contribution

It extends previous models by incorporating lifetime broadening self-consistently, enhancing the accuracy of charge transport predictions in molecular junctions.

Findings

Self-consistent approach improves agreement with hierarchical equations-of-motion results.

Method accurately describes charge transport under strong electron-vibrational coupling.

The approach can be simplified to previous theories under certain conditions.

Abstract

Marcus and Landauer-Buttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion (HEOM) results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalised theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.