Crossover from adiabatic to antiadiabatic phonon-assisted tunneling in single-molecule transistors

Abstract

The crossover between two customary limits of phonon-assisted tunneling, the adiabatic and antiadiabatic regimes, is studied systematically in the framework of a minimal model for molecular devices: a resonant level coupled by displacement to a localized vibrational mode. Conventionally associated with the limits where the phonon frequency is either sufficiently small or sufficiently large as compared to the bare electronic hopping rate, we show that the crossover between the two regimes is governed for strong electron-phonon interactions primarily by the polaronic shift rather than the phonon frequency. In particular, the perturbative adiabatic limit is approached only as the bare hopping rate Γexceeds the polaronic shift, leaving an extended window of couplings where Γwell exceeds the phonon frequency and yet the physics is basically that of the antiadiabatic regime. We term this intermediate regime the extended antiadiabatic regime. The effective low-energy Hamiltonian in the traditional and the extended antiadiabatic regime is shown to be the (purely fermionic) interacting resonant-level model, with parameters that we extract from numerical renormalization-group calculations. The extended antiadiabatic regime is followed in turn by a true crossover region where the polaron gets progressively undressed. The renormalized tunneling rate, which serves as the low-energy scale in the problem and thus sets the width of the tunneling resonance, is found to follow an approximate scaling form on going from the adiabatic to the antiadiabatic regime. Charging properties are governed by two distinct mechanisms at the extended antiadiabatic and into the crossover region, giving rise to distinctive shoulders in the low-temperature conductance as a function of gate voltage.

arXiv comment19 pages, 14 figures

References in corpus (24)

• The numerical renormalization group method for quantum impurity systems
• Molecular Transport Junctions: Vibrational Effects
• The Kondo effect in C${}_{60}$ single-molecule transistors
• Real-time path integral approach to nonequilibrium many-body quantum system
• Inelastic electron tunneling via molecular vibrations in single-molecule transistors
• Franck-Condon blockade in suspended carbon nanotube quantum dots
• Tunneling in suspended carbon nanotubes assisted by longitudinal phonons
• Tuning the Kondo effect with a mechanically controllable break junction
• Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime
• Many Body Effects on the Transport Properties of Single-Molecule Devices
• Anderson impurity in pseudo-gap Fermi systems
• Numerical Renormalization Group Study of the Anderson-Holstein Impurity Model
• Current-induced nonequilibrium vibrations in single-molecule devices
• Pair tunneling through single molecules
• Vibration-induced correction to the current through a single molecule
• Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions
• Quantum transport through a deformable molecular transistor
• Bistability signatures in nonequilibrium charge transport through molecular quantum dots
• Theory of a resonant level coupled to several conduction electron channels in equilibrium and out-of-equilibrium
• Transient dynamics of a molecular quantum dot with a vibrational degree of freedom
• Phonon-assisted tunneling and two-channel Kondo physics in molecular junctions
• Kondo effect and channel mixing in oscillating molecules
• On the applicability of bosonization and the Anderson-Yuval methods at the strong-coupling limit of quantum impurity problems
• Quantum quenches and driven dynamics in a single-molecule device

Cited by in corpus (26)

• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
• Influence of vibrational modes on the quantum transport through a nano-device
• The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation
• Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling
• Renormalization in periodically driven quantum dots
• Functional renormalization group study of the Anderson--Holstein model
• Thermoelectric effects in molecular quantum dots with contacts
• Nonequilibrium thermoelectric transport through vibrating molecular quantum dots
• Inelastic electron tunneling spectroscopy for probing strongly correlated many-body systems by scanning tunneling microscopy
• Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots
• Electron transport in nanoscale junctions with local anharmonic modes
• Charge-vibration interaction effects in normal-superconductor quantum dots
• Functional renormalization group in Floquet space
• Exponential and power-law renormalization in phonon-assisted tunneling
• Finite frequency current noise in the Holstein model
• Influences of electron-phonon interaction on quantum transport through one quantum-dot system with side-coupled Majorana zero mode
• Neutrons on a surface of liquid helium
• Transient dynamics of an adiabatic NEMS
• Finite-bias transport through the interacting resonant level model coupled to a phonon mode -- a functional renormalization group study
• Quantum transport through a molecular level: a scattering states numerical renormalisation group study
• Realizing the interacting resonant level model using a quantum dot detector
• Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems
• Anti-adiabatic evolution in quantum-classical hybrid system
• Charge density wave breakdown in a heterostructure with electron-phonon coupling
• Particle-hole Symmetric Slave Boson Method for the Mixed Valence Problem