From Liouville to Landauer: Electron transport and the bath assumptions made along the way

A generalized quantum master equation approach is introduced to describe electron transfer in molecular junctions that spans both the off-resonant (tunneling) and resonant (hopping) transport regimes. The model builds on prior insights from scattering theory but is not limited to a certain parameter range with regard to the strength of the molecule-electrode coupling. The framework is used to study the simplest case of energy and charge transfer between the molecule and the electrodes for a single site noninteracting Anderson model in the limit of symmetric and asymmetric coupling between the molecule and the electrodes. In the limit of elastic transport, the Landauer result is recovered for the current by invoking a single active electron Ansatz and a binary collision approximation for the memory kernel. Inelastic transport is considered by allowing the excitation of electron-hole pairs in the electrodes in tandem with charge transport. In the case of low bias voltages where the Fermi levels of the electrodes remain below the molecular state, it is shown that the current arises from tunneling and the molecule remains neutral. However, once the threshold is reached for aligning the fermi level of one electrode with the molecular orbital, a small amount of charge transfer occurs with a negligible amount of hopping current. While inelasticity in the current has a minimal impact on the shape of the current-voltage curve in the case of symmetric electrode coupling, the results for a slight asymmetry in coupling demonstrate complete charge transfer and a significant drop in current. These results provide encouraging confirmation that the framework can describe charge transport across a wide range of electrode-molecule coupling and provide a unique perspective for developing new master equation treatments for energy and charge transport in molecular junctions. An extension of this work to account for inelastic scattering from electron-vibrational coupling at the molecule is straightforward and will be the subject of subsequent work.