Theory of the Franck-Condon blockade regime

Abstract

Strong coupling of electronic and vibrational degrees of freedom entails a low-bias suppression of the current through single-molecule devices, termed Franck-Condon blockade. In the limit of slow vibrational relaxation, transport in the Franck-Condon-blockade regime proceeds via avalanches of large numbers of electrons, which are interrupted by long waiting times without electron transfer. The avalanches consist of smaller avalanches, leading to a self-similar hierarchy which terminates once the number of transferred electrons per avalanche becomes of the order of unity. Experimental signatures of self-similar avalanche transport are strongly enhanced current (shot) noise, as expressed by giant Fano factors, and a power-law noise spectrum. We develop a theory of the Franck-Condon-blockade regime with particular emphasis on effects of electron cotunneling through highly excited vibrational states. As opposed to the exponential suppression of sequential tunneling rates for low-lying vibrational states, cotunneling rates suffer only a power-law suppression. This leads to a regime where cotunneling dominates the current for any gate voltage. Including cotunneling within a rate-equation approach to transport, we find that both the Franck-Condon blockade and self-similar avalanche transport remain intact in this regime. We predict that cotunneling leads to absorption-induced vibrational sidebands in the Coulomb-blockaded regime as well as intrinsic telegraph noise near the charge degeneracy point.

20 pages, 10 figures; minor changes, version published in Phys. Rev. B

References in corpus (8)

• Franck-Condon blockade and giant Fano factors in transport through single molecules
• The Kondo effect in C${}_{60}$ single-molecule transistors
• Electrical generation and absorption of phonons in carbon nanotubes
• Vibrational sidebands and dissipative tunneling in molecular transistors
• Current-induced nonequilibrium vibrations in single-molecule devices
• Vibrational Sidebands and Kondo-effect in Molecular Transistors
• Full counting statistics of strongly non-Ohmic transport through single molecules
• Effects of charge-dependent vibrational frequencies and anharmonicities in transport through molecules

Cited by in corpus (28)

• Molecular Transport Junctions: Vibrational Effects
• Franck-Condon blockade in suspended carbon nanotube quantum dots
• Tunneling through molecules and quantum dots: master-equation approaches
• Kinetic Equations for Transport Through Single-Molecule Transistors
• Transport in molecular states language: Generalized quantum master equation approach
• Charge transport through single molecules, quantum dots, and quantum wires
• Self-consistent theory of molecular switching
• Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction
• Cotunneling and non-equilibrium magnetization in magnetic molecular monolayers
• Vibrational Excitations in Weakly Coupled Single-Molecule Junctions: A Computational Analysis
• Transport through quantum-dot spin valves containing magnetic impurities
• Semi-classical dynamics of nano-electromechanical systems
• Distortion blockade in classical nano-electromechanical resonator
• Nonequilibrium charge-Kondo transport through negative-U molecules
• Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors
• Nonequilibrium resonant spectroscopy of molecular vibrons
• Sub-Poissonian phononic population in a nanoelectromechanical system
• Coherent properties of nano-electromechanical systems
• Cooling a vibrational mode coupled to a molecular single-electron transistor
• Inelastic cotunneling in quantum dots and molecules with weakly broken degeneracies
• Quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator
• Influence of spin waves on transport through a quantum-dot spin valve
• Vibrational Coherences in Nano-Elastic Tunneling
• Coulomb Blockade of a Three-terminal Quantum Dot
• Mechanical feedback in the high-frequency limit
• Coulomb blockade for an oscillating tunnel junction
• Counting statistics for mesoscopic conductors with internal degrees of freedom
• Phonon-assisted and magnetic field induced Kondo tunneling in single molecular devices