Thermodynamics of the polaron master equation at finite bias
arXiv:1409.6480 · doi:10.1063/1.4916359
Abstract
We study coherent transport through a double quantum dot. Its two electronic leads induce electronic matter and energy transport and a phonon reservoir contributes further energy exchanges. By treating the system-lead couplings perturbatively, whereas the coupling to vibrations is treated non-perturbatively in a polaron-transformed frame, we derive a thermodynamic consistent low-dimensional master equation. When the number of phonon modes is finite, a Markovian description is only possible when these couple symmetrically to both quantum dots. For a continuum of phonon modes however, also asymmetric couplings can be described with a Markovian master equation. We compute the electronic current and dephasing rate. The electronic current enables transport spectroscopy of the phonon frequency and displays signatures of Franck-Condon blockade. For infinite external bias but finite tunneling bandwidths, we find oscillations in the current as a function of the internal bias due to the electron-phonon coupling. Furthermore, we derive the full fluctuation theorem and show its identity to the entropy production in the system.
17 pages, 5 figures, shortened presentation, added references, to appear in JCP
References in corpus (27)
- Spin qubits in graphene quantum dots
- Molecular Transport Junctions: Vibrational Effects
- Franck-Condon blockade and giant Fano factors in transport through single molecules
- Real-time path integral approach to nonequilibrium many-body quantum system
- Thermoelectric energy harvesting with quantum dots
- Franck-Condon blockade in suspended carbon nanotube quantum dots
- Theory of the Franck-Condon blockade regime
- Experimental Evidence for Quantum Interference and Vibrationally Induced Decoherence in Single-Molecule Junctions
- Kinetic Equations for Transport Through Single-Molecule Transistors
- Resonant Electron Transport in Single-Molecule Junctions: Vibrational Excitation, Rectification, Negative Differential Resistance and Local Cooling
- Phonon-assisted current noise in molecular junctions
- Cooling mechanisms in molecular conduction junctions
- Electron-phonon interaction and full counting statistics in molecular junctions
- Inelastic effects in molecular junction transport: Scattering and self-consistent calculations for the Seebeck coefficient
- Bistability signatures in nonequilibrium charge transport through molecular quantum dots
- Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction
- Tight coupling in thermal Brownian motors
- Nonlinear effects of phonon fluctuations on transport through nanoscale junctions
- Weak coupling approximations in non-Markovian Transport
- Vibrational cooling and thermoelectric response of nanoelectromechanical systems
- Single electron transistor strongly coupled to vibrations: Counting Statistics and Fluctuation Theorem
- Nonequilibrium charge-Kondo transport through negative-U molecules
- Current Noise in Single-Molecule Junctions Induced by Electronic-Vibrational Coupling
- Vibrationally Induced Decoherence in Single-Molecule Junctions
- Decoherence in semiconductor cavity QED systems due to phonon scattering
- Vibrationally-mediated molecular transistors
- Spectroscopy of the transition-rate matrix for molecular junctions: dynamics in the Franck-Condon regime
Cited by in corpus (6)
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- Qubit absorption refrigerator at strong coupling
- Quantum Thermodynamics with Degenerate Eigenstate Coherences
- Vibrational effects in charge transport through a molecular double quantum dot
- Lifting the Franck-Condon blockade in driven quantum dots
- Non-equilibrium boundary driven quantum systems: models, methods and properties