Vibrational sidebands and dissipative tunneling in molecular transistors

TL;DR

This paper investigates how vibrational damping affects electron transport in molecular transistors, revealing a crossover from quantum to classical behavior influenced by environmental coupling, with results aligning with experimental data.

Contribution

It introduces a model incorporating frequency-dependent damping to analyze vibrational sidebands and tunneling in molecular devices, extending previous models with a realistic substrate interaction.

Findings

Transport exhibits Frank-Condon steps at high Q

Crossover to classical regime at low Q

Qualitative agreement with experiments on C60 devices

Abstract

Transport through molecular devices with strong coupling to a single vibrational mode is considered in the case where the vibration is damped by coupling to the environment. We focus on the weak tunneling limit, for which a rate equation approach is valid. The role of the environment can be characterized by a frictional damping term $\mysig(\omega)$ and corresponding frequency shift. We consider a molecule that is attached to a substrate, leading to frequency-dependent frictional damping of the single oscillator mode of the molecule, and compare it to a reference model with frequency-independent damping featuring a constant quality factor $Q$. For large values of $Q$, the transport is governed by tunneling between displaced oscillator states giving rise to the well-known series of the Frank-Condon steps, while at small $Q$, there is a crossover to the classical regime with an energy gap given by the classical displacement energy. Using realistic values for the elastic properties of the substrate and the size of the molecule, we calculate $I$-$V$ curves and find qualitative agreement between our theory and recent experiments on $C_{60}$ single-molecule devices.