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Roles of nonlocal electron-phonon coupling on the electrical conductivity and Seebeck coefficient: A time-dependent DMRG study
Yufei Ge, Weitang Li, Jiajun Ren, and Zhigang Shuai
Phys. Rev. B 110, 035201 – Published 3 July 2024
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Abstract
Organic molecular materials are potential high-performance thermoelectric materials. Theoretical understanding of thermoelectric conversion in organic materials is essential for rational molecular design for efficient energy conversion materials. In organic materials, nonlocal electron-phonon coupling plays a vital role in charge transport and leads to complex transport mechanisms, including hopping, phonon assisted, band, and transient localization. In this work, based on the time-dependent density matrix renormalization group method, we look at the role of nonlocal electron-phonon coupling on the thermoelectric conversion in organic systems described by the Holstein-Peierls model. We calculate the current-current correlation and the heat current-current correlation functions. We find that (i) nonlocal electron-phonon coupling has a very weak influence on the Seebeck coefficient because of the cancellation between the heat current-current correlation function and the current-current correlation function, but it has a strong influence on the conductivity through dynamic disorders; and (ii) doping concentration has a strong influence on both the conductivity and Seebeck coefficient, and the optimal doping ratio to reach the highest power factor is 3%–10% fillings when the Holstein-Peierls model is valid. These findings suggest that we can design organic materials with higher power factors by first enhancing mobility through rational design, and then searching for the optimal doping ratio.
- Received 19 December 2023
- Revised 1 June 2024
- Accepted 17 June 2024
DOI:https://doi.org/10.1103/PhysRevB.110.035201
©2024 American Physical Society
Physics Subject Headings (PhySH)
- Research Areas
Electron-phonon couplingSeebeck effect
- Techniques
Density matrix renormalization group
Condensed Matter, Materials & Applied Physics
Authors & Affiliations
Yufei Ge1, Weitang Li2, Jiajun Ren3, and Zhigang Shuai4,*
- 1MOE Key Laboratory on Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, China
- 2Tencent Quantum Lab, Tencent, Shenzhen, 518057 Guangdong, China
- 3MOE Key Laboratory of Theoretical and Computational Photochemistry, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
- 4School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172 Guangdong, China
- *Contact author: shuaizhigang@cuhk.edu.cn
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Issue
Vol. 110, Iss. 3 — 15 July 2024
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Images
Figure 1
Schematic diagram of the numerical calculation progress. Here, we map the Holstein-Peierls model to the tensors in the DMRG calculation. If we consider two local vibration modes in each molecular and nearest-neighbor nonlocal vibration (red dotted box), we can align the tensors (sites) of electrons, nonlocal vibrations, and local vibrations as presented above.
Figure 2
Five transport regimes in organic materials. The yellow part is the hopping regime, where and ; the purple part is the phonon-assisted regime, where and is comparable to or larger than ; the blue part is the band regime, where and ; the green part is the transient localization regime, where and is comparable to or larger than ; the white part is the intermediate regime, where and . The gray dashed lines (I), (II), and (III) correspond to the parameter selection in Fig.3. The black crosses correspond to the representative parameters of five transport regimes, which are adopted in Figs.4, 5, 6.
Figure 3
Influence of nonlocal electron-phonon coupling on conductivity , Seebeck coefficient and mean free path under different local electron-phonon couplings. (a)–(c), (d)–(f), and (g)–(i) correspond to strong, intermediate, and weak local electron-phonon coupling, respectively. Here, and .
Figure 4
One-particle spectral density function when in (a) hopping regime, (b) intermediate regime 1, (c) band regime, (d) phonon-assisted regime, (e) intermediate regime 2, and (f) transient localization regime.
Figure 5
Temperature dependence of conductivity and Seebeck coefficient in different transport regimes. Here, . Note that in (a) and (b) and ; in (c) and (d) and ; in (e) and (f) and .
Figure 6
Dependence of conductivity , Seebeck coefficient and power factor on doping ratio when . (a)–(c) correspond to electron doping and (d)–(f) correspond to hole doping.
Figure 7
(a),(b) Convergence of virtual bond dimension ; (c),(d) convergence of the size of the nonlocal phonon basis ; and (e),(f) convergence of the size of local phonon basis in our work.
