Effect of broadening in the weak coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

TL;DR

This paper explores how vibrational excitation levels in molecular junctions and quantum dot systems increase as electronic-vibrational coupling weakens, especially under high bias, influenced by environmental broadening effects.

Contribution

It reveals the counterintuitive increase in vibrational excitation with decreasing coupling strength in the weak coupling limit, considering environmental broadening effects.

Findings

Vibrational excitation increases as coupling decreases at high bias.

Environmental effects like electrode hybridization and thermal fluctuations significantly influence vibrational behavior.

The results are applicable to both molecular junctions and quantum dot circuit QED systems.

Abstract

We investigate the nonequilibrium population of a vibrational mode in the steady state of a biased molecular junction, using a rate equation approach. We focus on the limit of weak electronic-vibrational coupling and show that, in the resonant transport regime and for sufficiently high bias voltages, the level of vibrational excitation increases with decreasing coupling strength, assuming a finite and non-zero value. An analytic behavior with respect to the electronic-vibrational coupling strength is only observed if the influence of environmental degrees of freedom is explicitly taken into account. We consider the influence of three different types of broadening: hybridization with the electrodes, thermal fluctuations and the coupling to a thermal heat bath. Our results apply to vibrationally coupled electron transport through molecular junctions but also to quantum dots coupled to a microwave cavity, where the photon number can be expected to exhibit a similar behavior.