Vibrational sidebands and dissipative tunneling in molecular transistors

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 $\mysig(ω)$ 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.

Major revisions and additions. 10 pages, 9 figures

Cited by in corpus (13)

• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Tunneling in suspended carbon nanotubes assisted by longitudinal phonons
• Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
• Shot Noise of a Quantum Shuttle
• Current noise in a vibrating quantum dot array
• Single-electron Tunneling with Strong Mechanical Feedback
• The charge shuttle as a nanomechanical ratchet
• Effects of charge-dependent vibrational frequencies and anharmonicities in transport through molecules
• Josephson current through a molecular transistor in a dissipative environment
• Magnetoconductance through a vibrating molecule in the Kondo regime
• Low frequency current noise of the single-electron shuttle
• Dissipative tunneling and orthogonality catastrophe in molecular transistors
• Dynamics of Shuttle Devices