A Generalized Landauer Approach for Electron Transport in a Single Molecule

TL;DR

This paper introduces a quaternion-inspired formalism to evaluate electron transport in single molecules, effectively capturing both ballistic and co-tunneling mechanisms across various coupling regimes.

Contribution

The authors develop a generalized Landauer approach using a Dyson series and quaternion formalism to unify treatment of different transport mechanisms in single-molecule systems.

Findings

Applicable to weak, strong, and intermediate coupling regimes

Successfully describes transport in conjugated and saturated molecules

Integrates ab initio quantum chemical calculations for level adjustments

Abstract

We present a quaternion-inspired formalism specifically developed to evaluate the electric current that traverses a single molecule subjected to an externally applied voltage. The molecule of interest is covalently connected to two small metallic clusters, forming an extended molecule complex. The quaternion approach allows for an integrated treatment of the charge transport in single molecules where both ballistic and co-tunneling (coherent) mechanisms are taken on equal footing, although only in the latter case the presence of eventual transient charged states of the system needs to be considered. We use a Dyson series to obtain a generalized Fermi golden rule, from which we derive an expression for the net current the two electrodes: in doing this, we take into account all possible transitions between electronic states localized at the electrodes and levels in the extended molecule complex. In fact, one can apply the method to the entire range of coupling regimes, not only in the weak or strong cases, but also in intermediate situations, where ballistic and co-tunneling processes compete with each other. We also discuss initial results of the application of this formalism to the description of the electronic transport in two small organic molecules representative of two different limit situations. In the first case, a conjugated molecule (where spatially delocalized molecular orbitals favor ballistic contributions) is considered, and in the second, the current traverses a saturated hydrocarbon (whose structure should contain more localized molecular orbitals). In both cases, we fully describe the field-induced self-adjustment of the electronic levels of the extended molecule complex at an ab initio quantum chemical level, using density functional theory.