Tunneling through molecules and quantum dots: master-equation approaches

Abstract

An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equations derived by Wangsness, Bloch, and Redfield and by Koenig et al. are equivalent. The roles of the large-reservoir and Markov approximations are clarified. The Markov approximation is traced back to nonzero bias voltage and temperature, whereas interactions and the corresponding rapid relaxation in the leads are shown to be irrelevant for the transport under certain conditions. It is explained why the T-matrix formalism gives incomplete results except for diagonal density operators and to second order in the tunneling amplitudes. The time-convolutionless master equation is adapted to tunneling problems and a diagrammatic scheme for generating arbitrary orders in the tunneling amplitudes is developed.

13 pages including 5 figures

References in corpus (15)

• Molecular Transport Junctions: Vibrational Effects
• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Theory of the Franck-Condon blockade regime
• Shot noise in tunneling transport through molecules and quantum dots
• Theory for transport through a single magnetic molecule: Endohedral N@C60
• Berry-phase blockade in single-molecule magnets
• Cotunneling and non-equilibrium magnetization in magnetic molecular monolayers
• Time-convolutionless master equation for mesoscopic electron-phonon systems
• Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors
• Coulomb Gas on the Keldysh Contour: Anderson-Yuval-Hamann representation of the Nonequilibrium Two Level System
• Linear and nonlinear transport across carbon nanotube quantum dots
• Sequential Tunneling through Molecular Spin Rings
• Theory of shot noise in single-walled metallic carbon nanotubes weakly coupled to nonmagnetic and ferromagnetic leads
• Berry-phase effects in transport through single Jahn-Teller molecules
• Gauge Theory for the Rate Equations: Electrodynamics on a Network

Cited by in corpus (41)

• Kinetic Equations for Transport Through Single-Molecule Transistors
• Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Transport in molecular states language: Generalized quantum master equation approach
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Spin effects in transport through single-molecule magnets in the sequential and cotunneling regimes
• Transport in a disordered tight-binding chain with dephasing
• Strongly nonlinear thermovoltage and heat dissipation in interacting quantum dots
• A self-consistent quantum master equation approach to molecular transport
• Cavity-coupled double-quantum dot at finite bias: analogy with lasers and beyond
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
• The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
• Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors
• Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling
• Dephasing-assisted transport in linear triple quantum dots
• Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit - divergences and resolution
• Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings
• Current noise cross correlation mediated by Majorana bound states
• Coherent properties of nano-electromechanical systems
• QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
• Superradiance-like Electron Transport through a Quantum Dot
• Memristive properties of single-molecule magnets
• A diagrammatic description of the equations of motion, current, and noise within the second-order von Neumann approach
• Inelastic cotunneling in quantum dots and molecules with weakly broken degeneracies
• Relaxation of quantum dots in a magnetic field at finite bias -- charge, spin and heat currents
• Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach
• Enhanced current noise correlations in a Coulomb-Majorana device
• Effects of magnetic field and transverse anisotropy on full counting statistics in single-molecule magnet
• Spin current and polarization reversal through a single-molecule magnet with ferromagnetic electrodes
• Controlling the conductance of molecular junctions using proton transfer reactions: A theoretical model study
• Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations
• Violation of Onsager's theorem in approximate master equation approaches
• General scheme for stable single and multiatom nanomagnets according to symmetry selection rules
• Nonequilibrium quantum dynamics of the magnetic Anderson model
• Probing bath-induced entanglement in a qubit pair by measuring photon correlations
• Modeling the metastable dynamics of correlated structures
• Transport and semiclassical dynamics of coupled quantum dots interacting with a local magnetic moment
• Lifting the Franck-Condon blockade in driven quantum dots
• Spectroscopy of the transition-rate matrix for molecular junctions: dynamics in the Franck-Condon regime
• Charge order in an interacting monolayer under transverse bias
• Magnon cotunneling through a quantum dot