Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport
Abstract
Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi’s Golden Rule and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero transport rates and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.
- Authors:
-
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
- Publication Date:
- OSTI Identifier:
- 22415695
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 16; 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:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; DIFFUSION; ELECTRON-PHONON COUPLING; FLUCTUATIONS; MOBILITY; ORGANIC SEMICONDUCTORS; PHONONS; POLARONS; RELAXATION TIME; TEMPERATURE DEPENDENCE
Citation Formats
Lee, Chee Kong, Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Moix, Jeremy, and Cao, Jianshu. Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport. United States: N. p., 2015.
Web. doi:10.1063/1.4918736.
Lee, Chee Kong, Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Moix, Jeremy, & Cao, Jianshu. Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport. United States. https://doi.org/10.1063/1.4918736
Lee, Chee Kong, Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Moix, Jeremy, and Cao, Jianshu. 2015.
"Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport". United States. https://doi.org/10.1063/1.4918736.
@article{osti_22415695,
title = {Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport},
author = {Lee, Chee Kong and Centre for Quantum Technologies, National University of Singapore, 117543 Singapore and Moix, Jeremy and Cao, Jianshu},
abstractNote = {Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi’s Golden Rule and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero transport rates and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.},
doi = {10.1063/1.4918736},
url = {https://www.osti.gov/biblio/22415695},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 16,
volume = 142,
place = {United States},
year = {Tue Apr 28 00:00:00 EDT 2015},
month = {Tue Apr 28 00:00:00 EDT 2015}
}
Works referenced in this record:
Multi-quanta energy relaxation in a nonlinear quantum dimer coupled to a phonon bath
journal, September 2006
- Pouthier, Vincent
- Physica D: Nonlinear Phenomena, Vol. 221, Issue 1
Charge Transport in Organic Semiconductors
journal, April 2007
- Coropceanu, Veaceslav; Cornil, Jérôme; da Silva Filho, Demetrio A.
- Chemical Reviews, Vol. 107, Issue 4
A Structure-Based Model of Energy Transfer Reveals the Principles of Light Harvesting in Photosystem II Supercomplexes
journal, June 2013
- Bennett, Doran I. G.; Amarnath, Kapil; Fleming, Graham R.
- Journal of the American Chemical Society, Vol. 135, Issue 24
Conformational Disorder and Ultrafast Exciton Relaxation in PPV-family Conjugated Polymers
journal, January 2009
- Dykstra, Tieneke E.; Hennebicq, Emmanuelle; Beljonne, David
- The Journal of Physical Chemistry B, Vol. 113, Issue 3
Optimization of Exciton Trapping in Energy Transfer Processes
journal, December 2009
- Cao, Jianshu; Silbey, Robert J.
- The Journal of Physical Chemistry A, Vol. 113, Issue 50
Efficient Energy Transfer in Light-Harvesting Systems, III: The Influence of the Eighth Bacteriochlorophyll on the Dynamics and Efficiency in FMO
journal, November 2011
- Moix, Jeremy; Wu, Jianlan; Huo, Pengfei
- The Journal of Physical Chemistry Letters, Vol. 2, Issue 24
Band-like temperature dependence of mobility in a solution-processed organic semiconductor
journal, August 2010
- Sakanoue, Tomo; Sirringhaus, Henning
- Nature Materials, Vol. 9, Issue 9
Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
journal, July 2015
- Wang, Chen; Ren, Jie; Cao, Jianshu
- Scientific Reports, Vol. 5, Issue 1
Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains
journal, February 2004
- Bednarz, M.; Malyshev, V. A.; Knoester, J.
- The Journal of Chemical Physics, Vol. 120, Issue 8
Exciton Migration in Molecular Crystals
journal, June 1971
- Grover, M.; Silbey, R.
- The Journal of Chemical Physics, Vol. 54, Issue 11
Anisotropic field effect mobility in single crystal pentacene
journal, June 2006
- Lee, J. Y.; Roth, S.; Park, Y. W.
- Applied Physics Letters, Vol. 88, Issue 25
A unified theory for charge-carrier transport in organic crystals
journal, March 2008
- Cheng, Yuan-Chung; Silbey, Robert J.
- The Journal of Chemical Physics, Vol. 128, Issue 11
Theory of coherent resonance energy transfer
journal, September 2008
- Jang, Seogjoo; Cheng, Yuan-Chung; Reichman, David R.
- The Journal of Chemical Physics, Vol. 129, Issue 10
On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer
journal, June 2009
- Ishizaki, Akihito; Fleming, Graham R.
- The Journal of Chemical Physics, Vol. 130, Issue 23
Fluorescence depolarization in poly[2-methoxy-5-((2-ethylhexyl)oxy)-1,4-phenylenevinylene]: Sites versus eigenstates hopping
journal, January 2009
- Singh, Jaykrishna; Bittner, Eric R.; Beljonne, David
- The Journal of Chemical Physics, Vol. 131, Issue 19
Theory of multichromophoric coherent resonance energy transfer: A polaronic quantum master equation approach
journal, July 2011
- Jang, Seogjoo
- The Journal of Chemical Physics, Vol. 135, Issue 3
Electronic excitation dynamics in multichromophoric systems described via a polaron-representation master equation
journal, October 2011
- Kolli, Avinash; Nazir, Ahsan; Olaya-Castro, Alexandra
- The Journal of Chemical Physics, Vol. 135, Issue 15
Variational calculation of the dynamics of a two level system interacting with a bath
journal, March 1984
- Silbey, Robert; Harris, Robert A.
- The Journal of Chemical Physics, Vol. 80, Issue 6
Accuracy of second order perturbation theory in the polaron and variational polaron frames
journal, May 2012
- Lee, Chee Kong; Moix, Jeremy; Cao, Jianshu
- The Journal of Chemical Physics, Vol. 136, Issue 20
Criteria for the accuracy of small polaron quantum master equation in simulating excitation energy transfer dynamics
journal, December 2013
- Chang, Hung-Tzu; Zhang, Pan-Pan; Cheng, Yuan-Chung
- The Journal of Chemical Physics, Vol. 139, Issue 22
Efficient energy transfer in light-harvesting systems, I: optimal temperature, reorganization energy and spatial–temporal correlations
journal, October 2010
- Wu, Jianlan; Liu, Fan; Shen, Young
- New Journal of Physics, Vol. 12, Issue 10
A multi-site variational master equation approach to dissipative energy transfer
journal, July 2013
- Pollock, Felix A.; McCutcheon, Dara P. S.; Lovett, Brendon W.
- New Journal of Physics, Vol. 15, Issue 7
Coherent quantum transport in disordered systems: I. The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems
journal, August 2013
- Moix, Jeremy M.; Khasin, Michael; Cao, Jianshu
- New Journal of Physics, Vol. 15, Issue 8
Coherent quantum transport in disordered systems: II. Temperature dependence of carrier diffusion coefficients from the time-dependent wavepacket diffusion method
journal, April 2014
- Zhong, Xinxin; Zhao, Yi; Cao, Jianshu
- New Journal of Physics, Vol. 16, Issue 4
Theoretical description of quantum effects in multi-chromophoric aggregates
journal, August 2012
- Zimanyi, Eric N.; Silbey, Robert J.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1972
Theory of charge transport in organic crystals: Beyond Holstein’s small-polaron model
journal, June 2009
- Ortmann, Frank; Bechstedt, Friedhelm; Hannewald, Karsten
- Physical Review B, Vol. 79, Issue 23
Transient localization in crystalline organic semiconductors
journal, February 2011
- Ciuchi, S.; Fratini, S.; Mayou, D.
- Physical Review B, Vol. 83, Issue 8
First-principles calculations of anisotropic charge-carrier mobilities in organic semiconductor crystals
journal, April 2011
- Stehr, V.; Pfister, J.; Fink, R. F.
- Physical Review B, Vol. 83, Issue 15
Coherent and incoherent dynamics in excitonic energy transfer: Correlated fluctuations and off-resonance effects
journal, April 2011
- McCutcheon, Dara P. S.; Nazir, Ahsan
- Physical Review B, Vol. 83, Issue 16
Damping of Exciton Rabi Rotations by Acoustic Phonons in Optically Excited Quantum Dots
journal, January 2010
- Ramsay, A. J.; Gopal, Achanta Venu; Gauger, E. M.
- Physical Review Letters, Vol. 104, Issue 1
Relaxation Dynamics of Photoexcited Excitons in Rubrene Single Crystals Using Femtosecond Absorption Spectroscopy
journal, August 2012
- Tao, S.; Ohtani, N.; Uchida, R.
- Physical Review Letters, Vol. 109, Issue 9
Temperature-Dependent Mollow Triplet Spectra from a Single Quantum Dot: Rabi Frequency Renormalization and Sideband Linewidth Insensitivity
journal, August 2014
- Wei, Yu-Jia; He, Yu; He, Yu-Ming
- Physical Review Letters, Vol. 113, Issue 9
Temperature Dependent Fluorescence in Disordered Frenkel Chains: Interplay of Equilibration and Local Band-Edge Level Structure
journal, November 2003
- Bednarz, M.; Malyshev, V. A.; Knoester, J.
- Physical Review Letters, Vol. 91, Issue 21
Intrinsic Charge Transport on the Surface of Organic Semiconductors
journal, August 2004
- Podzorov, V.; Menard, E.; Borissov, A.
- Physical Review Letters, Vol. 93, Issue 8, Article No. 086602
Charge-Transport Regime of Crystalline Organic Semiconductors: Diffusion Limited by Thermal Off-Diagonal Electronic Disorder
journal, March 2006
- Troisi, Alessandro; Orlandi, Giorgio
- Physical Review Letters, Vol. 96, Issue 8
Quantum Transport of Slow Charge Carriers in Quasicrystals and Correlated Systems
journal, July 2006
- Trambly de Laissardière, Guy; Julien, Jean-Pierre; Mayou, Didier
- Physical Review Letters, Vol. 97, Issue 2
Elastomeric Transistor Stamps: Reversible Probing of Charge Transport in Organic Crystals
journal, March 2004
- Sundar, Vikram C.; Zaumseil, Jana; Podzorov, Vitaly
- Science, Vol. 303, Issue 5664, p. 1644-1646
Coherence Dynamics in Photosynthesis: Protein Protection of Excitonic Coherence
journal, June 2007
- Lee, H.; Cheng, Y. -C.; Fleming, G. R.
- Science, Vol. 316, Issue 5830
Charge Transport in Organic Semiconductors
journal, July 2007
- Coropceanu, Veaceslav; Cornil, Jerome; da Silva Filho, Demetrio A.
- ChemInform, Vol. 38, Issue 29
Efficient energy transfer in light-harvesting systems, I: optimal temperature, reorganization energy, and spatial-temporal correlations
text, January 2010
- Wu, Jianlan; Liu, Fan; Shen, Young
- arXiv
First principles calculations of anisotropic charge carrier mobilities in organic semiconductor crystals
text, January 2011
- Stehr, V.; Pfister, J.; Fink, R. F.
- arXiv
Efficient energy transfer in light-harvesting systems, III: The influence of the eighth bacteriochlorophyll on the dynamics and efficiency in FMO
preprint, January 2011
- Moix, Jeremy; Wu, Jianlan; Huo, Pengfei
- arXiv
A multi-site variational master equation approach to dissipative energy transfer
text, January 2012
- Pollock, Felix A.; McCutcheon, Dara P. S.; Lovett, Brendon W.
- arXiv
Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems
text, January 2013
- Moix, Jeremy M.; Khasin, Michael; Cao, Jianshu
- arXiv
Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
text, January 2014
- Wang, Chen; Ren, Jie; Cao, Jianshu
- arXiv
Temperature dependent fluorescence in disordered Frenkel chains: interplay of equilibration and local band-edge level structure
text, January 2003
- Bednarz, M.; Malyshev, V. A.; Knoester, J.
- arXiv
Intrinsic charge transport on the surface of organic semiconductors
text, January 2004
- Podzorov, V.; Menard, E.; Borissov, A.
- arXiv
Quantum transport of slow charge carriers in quasicrystals and correlated systems
text, January 2006
- De Laissardière, Guy Trambly; Julien, Jean-Pierre; Mayou, Didier
- arXiv
Works referencing / citing this record:
Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach
journal, May 2016
- Xu, Dazhi; Cao, Jianshu
- Frontiers of Physics, Vol. 11, Issue 4
Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
journal, July 2015
- Wang, Chen; Ren, Jie; Cao, Jianshu
- Scientific Reports, Vol. 5, Issue 1
Simulations of infrared and Raman spectra in solution using the fragment molecular orbital method
journal, January 2019
- Nakata, Hiroya; Fedorov, Dmitri G.
- Physical Chemistry Chemical Physics, Vol. 21, Issue 25
Brownian ratchets: How stronger thermal noise can reduce diffusion
journal, February 2017
- Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, Issue 2
Modeling the effects of molecular disorder on the properties of Frenkel excitons in organic molecular semiconductors
journal, September 2018
- Shi, Liang; Willard, Adam P.
- The Journal of Chemical Physics, Vol. 149, Issue 9
Polaron effects on the performance of light-harvesting systems: a quantum heat engine perspective
journal, January 2016
- Xu, Dazhi; Wang, Chen; Zhao, Yang
- New Journal of Physics, Vol. 18, Issue 2
Describing many-body localized systems in thermal environments
journal, June 2019
- Wu, Ling-Na; Schnell, Alexander; Tomasi, Giuseppe De
- New Journal of Physics, Vol. 21, Issue 6
Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
journal, February 2017
- Wang, Chen; Ren, Jie; Cao, Jianshu
- Physical Review A, Vol. 95, Issue 2
Steady-state entanglement and coherence of two coupled qubits in equilibrium and nonequilibrium environments
journal, April 2019
- Wang, Zhihai; Wu, Wei; Wang, Jin
- Physical Review A, Vol. 99, Issue 4
Polaron relaxation and charge dynamics near the mobility edge of a possible Wigner lattice of polarons
journal, July 2018
- Hettiarachchi, Gayan Prasad; Nishida, Yoshifumi; Masaki, Yusuke
- Physical Review B, Vol. 98, Issue 3
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition
journal, May 2016
- Chuang, Chern; Lee, Chee Kong; Moix, Jeremy M.
- Physical Review Letters, Vol. 116, Issue 19
Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
text, January 2014
- Wang, Chen; Ren, Jie; Cao, Jianshu
- arXiv
Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
text, January 2016
- Wang, Chen; Ren, Jie; Cao, Jianshu
- arXiv
Brownian ratchets: How stronger thermal noise can reduce diffusion
text, January 2017
- Spiechowicz, Jakub; Kostur, Marcin; Łuczka, Jerzy
- arXiv
Steady-state entanglement and coherence of the coupled qubit system in equilibrium and nonequilibrium environments
text, January 2018
- Wang, Zhihai; Wu, Wei; Wang, Jin
- arXiv
Nonequilibrium Energy Transfer at Nanoscale: A Unified Theory from Weak to Strong Coupling
journal, July 2015
- Wang, Chen; Ren, Jie; Cao, Jianshu
- Scientific Reports, Vol. 5, Issue 1
Molecular dynamics and charge transport in organic semiconductors: a classical approach to modeling electron transfer
journal, January 2017
- Pelzer, Kenley M.; Vázquez-Mayagoitia, Álvaro; Ratcliff, Laura E.
- Chemical Science, Vol. 8, Issue 4