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

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• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions
• 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
• Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order
• Transport Statistics of Interacting Double Dot Systems: Coherent and Non-Markovian Effects
• First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes
• Numerically exact, time-dependent study of correlated electron transport in model molecular junctions
• A self-consistent quantum master equation approach to molecular transport
• Quantum Transport through Nanostructures with Orbital Degeneracies
• Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
• Cavity-coupled double-quantum dot at finite bias: analogy with lasers and beyond
• Green function techniques in the treatment of quantum transport at the molecular scale
• Finite-frequency counting statistics of electron transport: Markovian Theory
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
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• The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
• Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
• Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Geometrical effects and signal delay in time-dependent transport at the nanoscale
• Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling
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• Coulomb interaction and transient charging of excited states in open nanosystems
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• Thermoelectrics in Coulomb-coupled quantum dots: Cotunneling and energy-dependent lead couplings
• Random transition-rate matrices for the master equation
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• Resonant and Kondo tunneling through molecular magnets
• Transport mirages in single-molecule devices
• Coherent properties of nano-electromechanical systems
• Sharp peaks in the conductance of double quantum dot and quantum dot spin-valve systems at high temperatures: A hierarchical quantum master equation approach
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• QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
• Time local master equation connecting the Born and Markov approximations
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• Dynamical multistability in a quantum-dot laser
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• Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
• Interaction effect on adiabatic pump of charge and spin in quantum dot
• The interplay between local and non-local master equations: exact and approximated dynamics
• Modeling of cotunneling in quantum dot systems
• Non-Monotonic Thermoelectric Currents and Energy Harvesting in Interacting Double Quantum-Dots
• A multilayer multiconfiguration time-dependent Hartree study of the nonequilibrium Anderson impurity model at zero temperature
• Motor effect in electron transport through a molecular junction with torsional vibrations
• Memristive properties of single-molecule magnets
• Open quantum systems beyond Fermi's golden rule: Diagrammatic expansion of the steady-state time-convolutionless master equation
• A diagrammatic description of the equations of motion, current, and noise within the second-order von Neumann approach
• Many-body non-equilibrium effects in all-electric electron spin resonance
• Inelastic cotunneling in quantum dots and molecules with weakly broken degeneracies
• Distribution of waiting times between electron cotunnelings
• Enhanced current noise correlations in a Coulomb-Majorana device
• Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach
• Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
• Duality for open fermion systems: energy-dependent weak coupling and quantum master equations
• Canyon of Current Suppression in an interacting two-level Quantum Dot
• Relaxation of quantum dots in a magnetic field at finite bias -- charge, spin and heat currents
• Quantum transport through single-molecule junctions with orbital degeneracies
• A Quasi-Classical Mapping Approach to Vibrationally Coupled Electron Transport in Molecular Junctions
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• Controlling the conductance of molecular junctions using proton transfer reactions: A theoretical model study
• Relaxation dynamics in double-spin systems
• Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism
• General scheme for stable single and multiatom nanomagnets according to symmetry selection rules
• Fluctuating-time and full counting statistics for quantum transport in a system with internal telegraphic noise
• Coherent Backaction of Quantum Dot Detectors: Qubit Isospin Precession
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• On the cotunneling regime of interacting quantum dots
• Generalized Master Equation Approach to Time-Dependent Many-Body Transport
• On the Accuracy of the Noninteracting Electron Approximation for Vibrationally Coupled Electron Transport
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• Probing bath-induced entanglement in a qubit pair by measuring photon correlations
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• Spin-orbit interaction induces charge beatings in a lightwave-STM single molecule junction
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• Time-convolutionless master equation: Perturbative expansions to arbitrary order and application to quantum dots
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• Current noise spectrum in a solvable model of tunneling Fermi-edge singularity
• Dynamical Magnetic and Nuclear Polarization in Complex Spin Systems: Semi-magnetic II-VI Quantum Dots
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• Synchronized coherent charge oscillations in coupled double quantum dots
• Exact description of fermionic reservoirs via purified damped ancillary fermions
• Time-dependent magnetotransport in semiconductor nanostructures via the generalized master equation
• Lindblad theory for incoherently-driven electron transport in molecular nanojunctions
• Berry-phase effect in single molecule magnets: analytical and numerical results