Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

Abstract

We present a novel hierarchical quantum master equation (HQME) approach which provides a numerically exact description of nonequilibrium charge transport in nanosystems with electronic-vibrational coupling. In contrast to previous work [Phys. Rev. B $94$, 201407 (2016)], the active vibrational degrees of freedom are treated in the reservoir subspace and are integrated out. This facilitates applications to systems with very high excitation levels, for example due to current-induced heating, while properties of the vibrational degrees of freedom, such as the excitation level and other moments of the vibrational distribution function, are still accessible. The method is applied to a generic model of a nanosystem, which comprises a single electronic level that is coupled to fermionic leads and a vibrational degree of freedom. Converged results are obtained in a broad spectrum of parameters, ranging from the nonadiabatic to the adiabatic transport regime. We specifically investigate the phenomenon of vibrational instability, that is, the increase of current-induced vibrational excitation for decreasing electronic-vibrational coupling. The novel HQME approach allows us to analyze the influence of level broadening due to both molecule-lead coupling and thermal effects. Results obtained for the first two moments suggest that the vibrational excitation is always described by a geometric distribution in the weak electronic-vibrational coupling limit.

References in corpus (90)

• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Phonon effects in molecular transistors: Quantum and classical treatment
• Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
• Inelastic transport theory from first-principles: methodology and applications for nanoscale devices
• Negative Differential Conductance and Hot Phonons in Suspended Nanotube Molecular Wires
• Real-time path integral approach to nonequilibrium many-body quantum system
• Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips
• Franck-Condon blockade in suspended carbon nanotube quantum dots
• Vibrational sidebands and dissipative tunneling in molecular transistors
• Exact quantum master equation via the calculus on path integrals
• Theory of the Franck-Condon blockade regime
• Tunneling in suspended carbon nanotubes assisted by longitudinal phonons
• A non-Markovian decoherence theory for double dot charge qubit
• Experimental Evidence for Quantum Interference and Vibrationally Induced Decoherence in Single-Molecule Junctions
• Resonant inelastic tunneling in molecular junctions
• Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
• Coherent coupling of a single spin to microwave cavity photons
• Coupling a quantum dot, fermionic leads and a microwave cavity on-chip
• Kinetic Equations for Transport Through Single-Molecule Transistors
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• The effect of inelastic processes on tunneling
• Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
• Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime
• Tunneling broadening of vibrational sidebands in molecular transistors
• Single electron-phonon interaction in a suspended quantum dot phonon cavity
• Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
• Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
• Modified-scaled hierarchical equation of motion approach for the study of quantum coherence in photosynthetic complexes
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Current-induced nonequilibrium vibrations in single-molecule devices
• Photon Emission from a Cavity-Coupled Double Quantum Dot
• Coherent electron-phonon coupling and polaron-like transport in molecular wires
• Theory of Vibrationally Inelastic Electron Transport through Molecular Bridges
• Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions
• Universal features of electron-phonon interactions in atomic wires
• Photon mediated interaction between distant quantum dot circuits
• Phonon-mediated negative differential conductance in molecular quantum dots
• Transport in molecular states language: Generalized quantum master equation approach
• Phonon-assisted current noise in molecular junctions
• Quantum Interference and Decoherence in Single-Molecule Junctions: How Vibrations Induce Electrical Current
• Electron-phonon interaction and full counting statistics in molecular junctions
• Out of equilibrium charge dynamics in a hybrid cQED architecture
• Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom
• Vibrational effects in laser driven molecular wires
• Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions
• Kondo memory in driven strongly-correlated quantum dots
• Multimode vibrational effects in single molecule conductance: A nonequilibrium Green's function approach
• Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions
• Transport through an Anderson impurity: Current ringing, non-linear magnetization and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations
• Resonant vibrations, peak broadening and noise in single molecule contacts: beyond the resonant tunnelling picture
• Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions
• Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
• Iterative summation of path integrals for nonequilibrium molecular quantum transport
• Bistability signatures in nonequilibrium charge transport through molecular quantum dots
• Phonon runaway in nanotube quantum dots
• Influence of vibrational modes on the quantum transport through a nano-device
• Full-counting statistics for molecular junctions: Fluctuation theorem and singularities
• Dynamic Jahn-Teller effect in electron transport through single C60 molecules
• Bias-Controlled Selective Excitation of Vibrational Modes in Molecular Junctions: A Route Towards Mode-Selective Chemistry
• Nonequilibrium phonon backaction on the current noise in atomic-sized junctions
• Nuclear wave function interference in single-molecule electron transport
• Effects of Herzberg--Teller vibronic coupling on coherent excitation energy transfer
• The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
• Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling
• Anomalous suppression of the shot noise in a nanoelectromechanical system
• Effect of nonadiabatic electronic-vibrational interactions on the transport properties of single-molecule junctions
• Nonequilibrium electron transport in strongly correlated molecular junctions
• Vibration-induced inelastic effects in the electron transport through multisite molecular bridges
• Sharp peaks in the conductance of double quantum dot and quantum dot spin-valve systems at high temperatures: A hierarchical quantum master equation approach
• Charge transport through a flexible molecular junction
• Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira-Leggett Hamiltonian
• Long-range Exchange Interaction in Triple Quantum Dots in the Kondo Regime
• Effect of broadening in the weak coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems
• Iterative path integral summation for nonequilibrium quantum transport
• Functional renormalization group study of the Anderson--Holstein model
• Phonon dynamics in correlated quantum systems driven away from equilibrium
• Transport signature of pseudo-Jahn-Teller dynamics in a single-molecule transistor
• Quantum transport in a resonant tunnel junction coupled to a nanomechanical oscillator
• Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots
• Vibrationally dependent electron-electron interactions in resonant electron transport through single-molecule junctions
• Kondo effect and the fate of bistability in molecular quantum dots with strong electron-phonon coupling
• Reappearance of Kondo Effect in Serially Coupled Symmetric Triple Quantum Dots
• Exponential and power-law renormalization in phonon-assisted tunneling
• Unified description of charge transfer mechanisms and vibronic dynamics in nanoscale junctions
• Local density of states on a vibrational quantum dot out of equilibrium
• Quantum transport through a molecular level: a scattering states numerical renormalisation group study

Cited by in corpus (36)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Green's function methods for single molecule junctions
• Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Current-induced bond rupture in single-molecule junctions
• Tree tensor network state approach for solving hierarchical equations of motion
• Using the Environment to Understand non-Markovian Open Quantum Systems
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Beyond Marcus theory and the Landauer-Buttiker approach in molecular junctions. II. A self-consistent Born approach
• Hierarchical quantum master equation approach to vibronic reaction dynamics at metal surfaces
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• Unraveling current-induced dissociation mechanisms in single-molecule junctions
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
• Nonequilibrium thermoelectric transport through vibrating molecular quantum dots
• Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions
• Generalized input-output method: A new route to quantum transport junctions
• Non-Adiabatic Effects of Nuclear Motion in Quantum Transport of Electrons: A Self-Consistent Keldysh-Langevin Study
• Strong coupling, weak impact: Phonon coupling versus pure dephasing in the photon statistics of cooperative emitters
• Kinetic Schemes in Open Interacting Systems
• Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes
• Efficient steady state solver for the hierarchical equations of motion approach: Formulation and application to charge transport through nanosystems
• Current-induced forces in nanosystems: A hierarchical equations of motion approach
• Time-dependent spectral functions of the Anderson impurity model in response to a quench with application to time-resolved photoemission spectroscopy
• Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach
• Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space
• Heat transfer in a nonequilibrium spin-boson model: A perturbative approach
• Coherent time-dependent oscillations and temporal correlations in triangular triple quantum dots
• Charge density wave breakdown in a heterostructure with electron-phonon coupling
• Testing bath correlation functions for open quantum dynamics simulations