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Title: Thermodynamics of the polaron master equation at finite bias

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.

Authors:
; ;  [1];  [2]
  1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin (Germany)
  2. Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg (Luxembourg)
Publication Date:
OSTI Identifier:
22415597
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 77 NANOSCIENCE AND NANOTECHNOLOGY; ASYMMETRY; ELECTRON-PHONON COUPLING; ENERGY TRANSFER; ENTROPY; FLUCTUATIONS; FRANCK-CONDON PRINCIPLE; MARKOV PROCESS; OSCILLATIONS; PHONONS; POLARONS; QUANTUM DOTS; SPECTROSCOPY; THERMODYNAMICS; TUNNEL EFFECT

Citation Formats

Krause, Thilo, Brandes, Tobias, Schaller, Gernot, and Esposito, Massimiliano. Thermodynamics of the polaron master equation at finite bias. United States: N. p., 2015. Web. doi:10.1063/1.4916359.
Krause, Thilo, Brandes, Tobias, Schaller, Gernot, & Esposito, Massimiliano. Thermodynamics of the polaron master equation at finite bias. United States. https://doi.org/10.1063/1.4916359
Krause, Thilo, Brandes, Tobias, Schaller, Gernot, and Esposito, Massimiliano. 2015. "Thermodynamics of the polaron master equation at finite bias". United States. https://doi.org/10.1063/1.4916359.
@article{osti_22415597,
title = {Thermodynamics of the polaron master equation at finite bias},
author = {Krause, Thilo and Brandes, Tobias and Schaller, Gernot and Esposito, Massimiliano},
abstractNote = {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.},
doi = {10.1063/1.4916359},
url = {https://www.osti.gov/biblio/22415597}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 13,
volume = 142,
place = {United States},
year = {Tue Apr 07 00:00:00 EDT 2015},
month = {Tue Apr 07 00:00:00 EDT 2015}
}