A semiclassical nonequilibrium Green's Function approach to electron transport in systems exhibiting electron-phonon couplings

Abstract

We formulate a semiclassical theory for electron transport in open quantum systems with electron-phonon interactions adequate for situations when the system's phonon dynamics is comparable with the electron transport timescale. Starting from the Keldysh non-equilibrium Green's function formalism we obtain equations of motion for the retarded and lesser electronic Green's functions including contributions due to the phonon dynamics up to second order in the electron-phonon coupling strength. The resulting equations assume that the system's phonon follow classical time-local dynamics with delta-correlated noise. We apply our method to the study of the charging/discharging of a periodically driven quantum dot, and a three-level model for a single-electron pump, analyzing the signatures in the transient current, electron population and process performance of the phonon dynamics. For these systems, we adopt the fluctuation-dissipation theorem and consider external harmonic driving of the phonon at frequencies comparable with the electron modulation, and different scenarios, varying electron-phonon coupling strength, coupling to the electron part of the system, and in phase and anti-phase driving. Our results illustrate that our method provides an efficient protocol to describe the effects of nuclear motion in ultrafast transient phenomena.

References in corpus (53)

• Time-dependent transport in interacting and non-interacting mesoscopic systems
• First-principles study of the phonon-limited mobility in n-type single-layer MoS2
• Molecular Transport Junctions: Vibrational Effects
• Real-time path integral approach to nonequilibrium many-body quantum system
• Electron-phonon effects and transport in carbon nanotubes
• Advances and challenges in single-molecule electron transport
• Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips
• Electronic Transport in Two-Dimensional Materials
• Acoustic phonon limited mobility in two-dimensional semiconductors: Deformation potential and piezoelectric scattering in monolayer MoS2 from first principles
• Experimental Evidence for Quantum Interference and Vibrationally Induced Decoherence in Single-Molecule Junctions
• Resonant inelastic tunneling in molecular junctions
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
• Born-Oppenheimer Dynamics, Electronic Friction, and the Inclusion of Electron-Electron Interactions
• Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
• Phonon-thermoelectric transistors and rectifiers
• Vibrational nonequilibrium effects in the conductance of single-molecules with multiple electronic states
• Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions
• Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions
• Efficiency fluctuations in quantum thermoelectric devices
• Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction
• Robust ultrafast currents in molecular wires through Stark shifts
• Conduction in molecular junctions: Inelastic effects
• Electron transfer across a thermal gradient
• A universal approach to quantum thermodynamics in the strong coupling regime
• Electron transfer at thermally heterogeneous molecule-metal interfaces
• Current-induced forces for nonadiabatic molecular dynamics
• Lessons on electronic decoherence in molecules from exact modeling
• Molecular junctions and molecular motors: Including Coulomb repulsion in electronic friction using nonequilibrium Green's functions
• Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots
• Electrothermal Transistor Effect and Cyclic Electronic Currents in Multithermal Charge Transfer Networks
• Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions
• Conductance of quantum spin Hall edge states from first principles: the critical role of magnetic impurities and inter-edge scattering
• Quantum Thermodynamics for Driven Dissipative Bosonic Systems
• Vibrational Relaxation at a Metal Surface: Electronic Friction Versus Classical Master Equations
• Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction
• Dynamical renormalization of electron-phonon coupling in conventional superconductors
• Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction
• Energetics of a driven Brownian harmonic oscillator
• Electronic friction in interacting systems
• Non-Adiabatic Effects of Nuclear Motion in Quantum Transport of Electrons: A Self-Consistent Keldysh-Langevin Study
• Electron transport in nanoscale junctions with local anharmonic modes
• Renormalization-group approach to superconductivity: from weak to strong electron-phonon coupling
• Density Functional Theory of the Hubbard-Holstein Model
• Reconciling perturbative approaches in phonon assisted transport junctions
• Flexoelectronic doping of the degenerate silicon and the correlated electron behavior
• Electron hopping heat transport in molecules
• A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators
• Electronic Friction Near Metal Surface: Incorporating Nuclear Quantum Effect with Ring Polymer Molecular Dynamics
• Evidence for Phonon-Assisted Intertube Electronic Transport in an Armchair Carbon Nanotube Film
• Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions
• Expectation values of single-particle operators in the random phase approximation ground state
• Optimal in situ electromechanical sensing of molecular species