Influence of vibrational modes on the quantum transport through a nano-device

Abstract

We use the recently proposed scattering states numerical renormalization group (SNRG) approach to calculate $I(V)$ and the differential conductance through a single molecular level coupled to a local molecular phonon. We also discuss the equilibrium physics of the model and demonstrate that the low-energy Hamiltonian is given by an effective interacting resonant level model. From the NRG level flow, we directly extract the effective charge transfer scale ${\Gamma }_{\mathrm{eff}}$ and the dynamically induced capacitive coupling $U_{\mathrm{eff}}$ between the molecular level and the lead electrons which turns out to be proportional to the polaronic energy shift $E_p$ for the regimes investigated here. The equilibrium spectral functions for the different parameter regimes are discussed. The additional phonon peaks at multiples of the phonon frequency $\w_0$ correspond to additional maxima in the differential conductance. Non-equilibrium effects, however, lead to significant deviations between a symmetric junction and a junction in the tunnel regime. The suppression of the current for asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed with a simple framework of a combination of (i) polaronic level shifts and (ii) the effective charge transfer scale ${\Gamma }_{\mathrm{eff}}$.

18 papers, 13 figures

References in corpus (23)

• The numerical renormalization group method for quantum impurity systems
• Molecular Transport Junctions: Vibrational Effects
• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Franck-Condon blockade in suspended carbon nanotube quantum dots
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Tunneling in suspended carbon nanotubes assisted by longitudinal phonons
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Kinetic Equations for Transport Through Single-Molecule Transistors
• Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime
• Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
• Quantum Interference and Decoherence in Single-Molecule Junctions: How Vibrations Induce Electrical Current
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
• Bistability signatures in nonequilibrium charge transport through molecular quantum dots
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• A Numerical Renormalization Group approach to Non-Equilibrium Green's Functions for Quantum Impurity Models
• Crossover from adiabatic to antiadiabatic phonon-assisted tunneling in single-molecule transistors
• The Coulomb Blockade in Quantum Boxes
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties

Cited by in corpus (45)

• 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
• Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
• Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
• Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime
• The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Spatial and temporal propagation of Kondo correlations
• Many-body Green's function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• Dressed tunneling approximation for electronic transport through molecular transistors
• Thermoelectric response of a correlated impurity in the nonequilibrium Kondo regime
• Full-counting statistics of energy transport of molecular junctions in the polaronic regime
• Iterative path integral summation for nonequilibrium quantum transport
• 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
• Thermodynamics of the polaron master equation at finite bias
• Inelastic electron tunneling spectroscopy for probing strongly correlated many-body systems by scanning tunneling microscopy
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• A Quasi-Classical Mapping Approach to Vibrationally Coupled Electron Transport in Molecular Junctions
• Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots
• Non-Adiabatic Effects of Nuclear Motion in Quantum Transport of Electrons: A Self-Consistent Keldysh-Langevin Study
• Transient dynamics in interacting nanojunctions within self-consistent perturbation theory
• Electron transport in nanoscale junctions with local anharmonic modes
• Charge-vibration interaction effects in normal-superconductor quantum dots
• Exponential and power-law renormalization in phonon-assisted tunneling
• From thermal equilibrium to nonequilibrium quench dynamics: A conserving approximation for the interacting resonant level
• Controlling the conductance of molecular junctions using proton transfer reactions: A theoretical model study
• Single-electron approach for time-dependent electron transport
• Transport properties of fully screened Kondo models
• Spin-vibronics in interacting nonmagnetic molecular nanojunctions
• Finite frequency current noise in the Holstein model
• Transient currents of a single molecular junction with a vibrational mode
• Influences of electron-phonon interaction on quantum transport through one quantum-dot system with side-coupled Majorana zero mode
• Local density of states on a vibrational quantum dot out of equilibrium
• Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model
• Magnetic field control of the Franck-Condon coupling of few-electron quantum states
• Nonlinear thermoelectric transport in single-molecule junctions: the effect of electron-phonon interactions
• 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
• Restoring the continuum limit in the time-dependent numerical renormalization group approach
• Realizing the interacting resonant level model using a quantum dot detector
• Charge density wave breakdown in a heterostructure with electron-phonon coupling
• Open Wilson chain numerical renormalization group approach to Green's functions