在本篇論文中，會針對有限長扶手椅型石墨烯奈米帶(Armchair Graphene
nanoribbons, AGNR)，和異質結構去進行討論。並特別專注在庫侖阻塞(Coulomb blockade)和包利自旋阻塞區域(Pauli spin blockade, PSB)的電荷傳輸。研究方法採用了考慮了局部化狀態內和局部化狀態間的庫侖相互作用的雙局部化態Hubbard模型。藉由這個模型，我們計算了串聯耦合拓樸態(serially coupled TS, SCTS)的穿隧電流。在有限長度AGNR我們發現經過串聯耦合拓樸態的穿隧電流具有負微分電導(negative differential conductance, NDC)的特性，且該電流是由拓樸態間庫侖交互作用產生而非拓樸態內庫侖交互作用。除此之外，我們還觀察到AGNR在非對稱系統中由於拓樸態間庫侖交互作用而出現的電流整流行為。最後，我們還發現了9-7-9 AGNR異質結構在包利自旋阻塞的配置中具有顯著的電流整流行為。

In this thesis, we will discuss finite-length and heterostructure AGNR with particular focus on charge transport in the Coulomb blockade and PSB regimes. The research approach employs a two-site Hubbard model considering both intra-site and inter-site Coulomb
interactions. By this model, we calculate the tunneling current of SCTS. We observe NDC characteristics in tunneling current through SCTS in finite-length AGNRs, and this current arises from inter-site Coulomb interactions rather than intra-site Coulomb interactions. Furthermore, we also observe current rectification behavior in the asymmetric junction of finite AGNRs because of inter-site Coulomb interactions. Finally, we also identified the significant current rectification behavior of SCTS of 9-7-9 AGNR heterostructures in the PSB configuration.

參考文獻
[1] A. K. Geim ,Graphene: Status and Prospects.Science324,1530-1534(2009).
[2] Geim, A., Grigorieva, I. Van der Waals heterostructures. Nature 499, 419–425 (2013)
[3] Shen, PC., Su, C., Lin, Y. et al. Ultralow contact resistance between semimetal and
monolayer semiconductors. Nature 593, 211–217 (2021).
[4] Iannaccone, G., Bonaccorso, F., Colombo, L. et al. Quantum engineering of transistors
based on 2D materials heterostructures. Nature Nanotech 13, 183–191 (2018).
[5] Cai, J., Ruffieux, P., Jaafar, R. et al. Atomically precise bottom-up fabrication of
graphene nanoribbons. Nature 466, 470–473 (2010).
[6] David M.-T. Kuo, Effects of metallic electrodes on the thermoelectric properties of
zigzag graphene nanoribbons with periodic vacancies. J. Phys.: Condens. Matter, 35,
305301 (2023).
[7] David M.-T. Kuo, Thermal rectification through the topological states of asymmetrical
length armchair graphene nanoribbons heterostructures with vacancies , Nanotechnology
34, 505401 (2023).
[8] Jacobse, P.H., Kimouche, A., Gebraad, T. et al. Electronic components embedded in a
single graphene nanoribbon. Nat Commun 8, 119 (2017).
[9] Brey, Luis and Herbert A. Fertig. Electronic states of graphene nanoribbons studied
with the Dirac equation. Physical Review B 73 (2006).
[10] Bolotin, Kirill I., K. J. Sikes, Zhigang Jiang, Martin Klíma, Geoffrey Fudenberg,
James C. Hone, Philip Kim and Horst L. Stormer. Ultrahigh electron mobility in suspended
graphene. Solid State Communications 146 (2008).
[11] Cao, Ting, Fangzhou Zhao and Steven G. Louie. Topological Phases in Graphene
Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains. Physical review
letters 119 7 (2017)
[12] Jiang, Jingwei and Steven G. Louie. Topology Classification using Chiral Symmetry
and Spin Correlations in Graphene Nanoribbons. Nano letters (2020)
[13] Lin, Kuan-Sen and Mei-Yin Chou. Topological Properties of Gapped Graphene
Nanoribbons with Spatial Symmetries. Nano letters 18 11 (2018)
27
[14] David M.-T. Kuo, Yia-Chung Chang, Contact Effects on Thermoelectric Properties of
Textured Graphene Nanoribbons, Nanomaterials, 12, 3357 (2022).
[15] David M. T. Kuo and Yia-Chung Chang, Tunneling current and emission spectrum of
a single electron transistor under optical pumping ,Phys. Rev. B 72, 085334 (2005)
[16] Sara M. Cronenwett et al. ,A Tunable Kondo Effect in Quantum Dots. Science 281,
540-544(1998).
[17] Tong, Chuyao, Annika Kurzmann, Rebekka Garreis, Wei Huang, Samuel Jele, Marius
Eich, L. P. Ginzburg, Christopher Mittag, Kenji Watanabe, Takashi Taniguchi, Klaus
Ensslin and Thomas Ihn. Pauli Blockade of Tunable Two-Electron Spin and Valley States
in Graphene Quantum Dots. Physical review letters 128 6 (2021)
[18] Liang, G., Neophytou, N., Lundstrom, M. S., & Nikonov, D. E. Contact effects in
graphene nanoribbon transistors. Nano letters, 8(7), 1819-1824.(2008)
[19] Michler, P., Imamoğlu, A., Mason, M. et al. Quantum correlation among photons from
a single quantum dot at room temperature . Nature 406, 968–970 (2000).
[20] K. Ono et al. ,Current Rectification by Pauli Exclusion in a Weakly Coupled Double
Quantum Dot System.Science297,1313-1317(2002).
[21] Rizzo, Daniel J., Jingwei Jiang, Dharati M. Joshi, Gregory Veber, Christopher
Bronner, Rebecca A. Durr, Peter H. Jacobse, Ting Cao, Alin Kalayjian, Henry Rodriguez,
Paul Butler, Ting Chen, Steven G Louie, Felix R. Fischer and Michael F. Crommie.
Rationally Designed Topological Quantum Dots in Bottom-Up Graphene Nanoribbons.
ACS Nano 15 (2021)
[22] Golor, Michael, Cornelie Koop, Thomas C. Lang, Stefan Wessel and M. Schmidt.
Magnetic correlations in short and narrow graphene armchair nanoribbons. Phys. Rev. Lett.
111, 085504 (2013)
[23] Fujita, Mitsutaka, Katsunori Wakabayashi, Kyoko Nakada and Koichi Kusakabe.
Peculiar Localized State at Zigzag Graphite Edge. Journal of the Physical Society of Japan
65 (1996)
[24] Nakada, Kyoko, Mitsutaka Fujita, Gene F Dresselhaus and Mildred S. Dresselhaus.
Edge state in graphene ribbons: Nanometer size effect and edge shape dependence.
Physical review. B, Condensed matter 54 24 (1996)
[25] Katsunori Wakabayashi, Mitsutaka Fujita, Hiroshi Ajiki, and Manfred Sigrist.
Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 59, 8271.(1998)
28
[26] López-Sancho, M. Pilar and M. Carmen Muñoz. Topologically protected edge and
confined states in finite armchair graphene nanoribbons and their junctions. Phys. Rev. B
104, 245402.(2021)
[27] Joost, J-P., Jauho, A-P., & Bonitz, M. Correlated Topological States in Graphene
Nanoribbon Heterostructures. Nano Letters, 19(12), 9045-9050.(2019)
[28] Kyoko Nakada, Mitsutaka Fujita, Gene Dresselhaus, and Mildred S. Dresselhaus.
Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys.
Rev. B 54, 17954.(1996)
[29] David M.-T. Kuo, Shiue-Yuan Shiau, and Yia-chung Chang. Theory of spin blockade,
charge ratchet effect, and thermoelectrical behavior in serially coupled quantum dot
system. Phys. Rev. B 84, 245303.(2011)
[30] David M. T. Kuo, Chih-Chieh Chen, and Yia-Chung Chang. Large enhancement in
thermoelectric efficiency of quantum dot junctions due to increase of level degeneracy.
Phys. Rev. B 95, 075432.(2017)
[31] Mark J. J. Mangnus, Felix R. Fischer, Michael F. Crommie, Ingmar Swart, and Peter
H. Jacobse. Charge transport in topological graphene nanoribbons and nanoribbon
heterostructures. Phys. Rev. B 105, 115424.(2022)
[32] Daniel J. Rizzo et al. ,Inducing metallicity in graphene nanoribbons via zero-mode
superlattices.Science369,1597-1603(2020).
[33] Yuki Matsuda, Wei-Qiao Deng, and William A. Goddard, III. Contact Resistance for
“End-Contacted” Metal−Graphene and Metal−Nanotube Interfaces from Quantum
Mechanics. J. Phys. Chem. C 2010, 114, 41, 17845–17850.(2010)
[34] Jonas Nyvold Pedersen, Benny Lassen, Andreas Wacker, and Matthias H. Hettler.
Coherent transport through an interacting double quantum dot: Beyond sequential
tunneling.Phys. Rev. B 75, 235314.(2007)