我們對石墨烯奈米帶（AGNRs）和異質結構的拓撲態（Topological States）在庫倫阻塞區域內的熱電性能進行了理論研究。採用包括局部內態和局部間態庫倫相互作用的雙局部態哈伯德模型，我們分析了這些材料的拓撲態。我們的探索集中在有限 AGNRs 的電導率（Ge）、塞貝克系數（S）和電子熱導率（ke）。有趣的是，我們發現在低溫下，塞貝克系數對多體效應的敏感性比電導率更大。此外，我們觀察到高溫下優化的塞貝克系數受到電子庫倫相互作用的影響較小，與 Ge 和 ke 相比。這項研究為我們理解庫倫阻塞效應對 AGNRs 和異質結構中拓撲態的電荷傳輸提供了寶貴的見解。

We conducted theoretical investigations into the thermoelectric properties of topological states in armchair graphene nanoribbons (AGNRs) and heterostructures within the Coulomb blockade regime. Employing a two-site Hubbard model that incorporates intra-localized state and inter-localized state Coulomb interactions, we analyzed the topological states (TS) of these materials. Our exploration focused on the electrical conductance (Ge), Seebeck coefficient (S), and electronic thermal conductance (ke) of finite AGNRs. Intriguingly, we discovered that at low temperatures, the Seebeck coefficient demonstrates greater sensitivity to many-body effects compared to conductance. Furthermore, we observed that the optimized Seebeck coefficient at high temperatures is less affected by electron Coulomb interactions in comparison to Ge and ke. This investigation provides valuable insights into understanding the Coulomb blockade effect on the charge transport of topological states in AGNRs and heterostructures.

[1] Novoselov, K.S.; Geim, A.K.; Morozov, S.V.; Jiang, D.; Zhang, Y.; Dubonos, S.V.; Grigorieva, I.V.; Firsov, A.A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666

[2] Geim, A.K. Graphene: Status and Prospects. Science 2009, 324, 1530

[3] Geim A.K.; Grigorieva, I.V. Van der Waals heterostructures. Nature 2013, 499, 419.

[4] Novoselov, K.S.; Mishchenko, A.; Carvalho, A.; Castro Neto, A.H.C. 2D materials and van der Waals heterostructures. Science 2016, 353, aac9439.

[5] Noshin, Maliha et al. “Thermal transport in defected armchair graphene nanoribbon: A molecular dynamics study.” TENCON 2017 - 2017 IEEE Region 10 Conference (2017): 2600-2603.

[6] Shen, P.C.; Su, C.; Lin, Y.X.; Chou, A.S.; Cheng, C.C.; Park, J.H.; Chiu, M.H.; Lu, A.Y.; Tang, H.L.; Tavakoli, M.M.; et al. Ultralow contact resistance between semimetal and monolayer semiconductors. Nature 2021, 593, 212.

[7] Iannaccone, G.; Bonaccorso, F.; Colombo, L.; Fiori, G. Quantum engineering of transistors based on 2D materials heterostructures. Nat. Nanotechnol. 2018, 13, 183

[8] Xiluan Wangab and Gaoquan Shi, An introduction to the chemistry of graphene. Phys. Chem. Chem. Phys., 2015, 17, 28484

[9] A. K. Geim and K. S. Novoselov. The rise of graphene. Nat. Mater. 6, 183 (2007).
[10] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene. Rev. Mod. Phys. 81, 109 – Published 14 January 2009

[11] H. Haug and A. P. Jauho. Quantum kinetics in transport and optics of semiconductors. (Springer, Heidelberg, 1996).

[12] Fritzsche, Hellmut, and Michael Pollak, eds. Hopping and related phenomena. Vol. 2. World Scientific, 1990.

[13] Kinkhabwala, Yusuf Amir. Quasi-continuous charge transfer via electron hopping. State University of New York at Stony Brook, 2005.

[14] Khademhosseini, Vahideh et al. “The Analysis of Coulomb Blockade in Fullerene Single Electron Transistor at Room Temperature.” (2017).

[15] Chen, YC., Cao, T., Chen, C. et al. Molecular bandgap engineering of bottom-up synthesized graphene nanoribbon heterojunctions. Nature Nanotech 10, 156–160 (2015).

[16] Son, Y.W.; Cohen, M.L.; Louie, S.G. Energy Gaps in Graphene Nanoribbons. Phys. Rev. Lett. 2006, 97, 216803.

[17] Cao, T.; Zhao, F.Z.; Louie, S.G. Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains. Phys. Rev. Lett. 2017, 119, 076401

[18] Lin, K.S.; Chou, M.Y. Topological properties of gapped graphene nanoribbons with spatial symmetries. Nano Lett. 2018, 18, 7254

[19] Jiang J.; Louie, S.G. Topology Classification using Chiral Symmetry and Spin Correlations in Graphene Nanoribbons. Nano. Lett. 2021, 21, 197
[20] Zhao, F.Z.; Cao, T.; Louie, S.G. Topological Phases in Graphene Nanoribbons Tuned by Electric Fields. Phys. Rev. Lett. 2021,127, 166401

[21] Pizzochero, M.; Tepliakov, N.V.; Arash, A.; Mostofi, A.A.; Kaxiras, E. Electrically Induced Dirac Fermions in Graphene Nanoribbons.Nano. Lett. 2021, 21, 9332

[22] Tepliakov, N.V.; Lischner, J.; Efthimios Kaxiras, E.; Mostofi A.A.; Pizzochero, M. Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons. Phys. Rev. Lett. 2023, 130, 026401

[23] Li, J., Sanz, S., Merino-Díez, N. et al. Topological phase transition in chiral graphene nanoribbons: from edge bands to end states. Nat Commun 12, 5538 (2021).

[24] Rizzo, D.J., Veber, G., Cao, T. et al. Topological band engineering of graphene nanoribbons. Nature 560, 204–208 (2018).

[25] Rizzo DJ, Jiang J, Joshi D, Veber G, Bronner C, Durr RA, Jacobse PH, Cao T, Kalayjian A, Rodriguez H, Butler P, Chen T, Louie SG, Fischer FR, Crommie MF. Rationally Designed Topological Quantum Dots in Bottom-Up Graphene Nanoribbons. ACS Nano. 2021 Dec 28;15(12):20633-20642.

[26] Kuo DMT. Thermal rectification through the topological states of asymmetrical length armchair graphene nanoribbons heterostructures with vacancies. Nanotechnology. 2023 Sep 29;34(50).

[27] Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M.S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 1996, 54, 17954.

[28] Wakabayashi, K.; Fujita, M.; Ajiki, H.; Sigrist, M. Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 1999,59, 8271
[29] Wakabayashi, K.; Sasaki, K.; Nakanishi, T.; Enoki, T. Electronic states of graphene nanoribbons and analytical solutions. Sci. Technol. Adv. Mater. 2010, 11, 054504

[30] H. Haug and A. P. Jauho. Quantum kinetics in transport and optics of semiconductors. (Springer, Heidelberg, 1996).

[31] David M. T. Kuo. Thermoelectric and electron heat rectification properties of quantum dot superlattice nanowire arrays. AIP Advances 10, 045222 (2020).

[32] David M. T. Kuo, Chih-Chieh Chen, Yia-Chung Chang. Large enhancement in thermoelectric efficiency of quantum dot junctions due to increase of level degeneracy. Phys. Rev. B 2017, 95, 075432.

[33] Mahan, G.D.; Sofo, J.O. The best thermoelectric. Proc. Natl. Acad. Sci. USA 1996, 93, 7436