簡易檢索 / 詳目顯示
| 研究生： |
邱義軒 Yi-Hsuan Chiu |
|---|---|
| 論文名稱： |
T_3\ 晶格模型弗洛凱拓樸邊緣態之探討 Study on the Floquet topological edge states of T_3 lattice model |
| 指導教授： |
欒丕綱
Pi-Gang Luan |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 光電科學與工程學系 Department of Optics and Photonics |
| 論文出版年： | 2025 |
| 畢業學年度： | 113 |
| 語文別： | 中文 |
| 論文頁數： | 56 |
| 中文關鍵詞： | T3晶格 、弗洛凱拓樸 、弗洛凱拓樸邊緣態 、T3弗洛凱拓樸 |
| 外文關鍵詞： | T_3 lattice, Floquet topological, Floquet topological edge states, T_3 Floquet topological |
| 相關次數： | 點閱：14 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本論文主要研究弗洛凱拓樸系統之拓樸不變量、邊界條件和手性邊緣態三者之間的關係。我們先透過淬火週期調制製造蜂窩晶格的弗洛凱拓樸模型，經過計算其不變量以此預測手性邊緣態數目，並各以不同邊界條件模擬其能帶圖，觀察是否如不變量所預期之結果，再以同週期調制方式制造 T_3\ 晶格的弗洛凱拓樸模型，計算其拓樸不變量，觀察不同的邊界條件對應的手性邊緣態是否如預期，與蜂窩晶格的弗洛凱模型有何異同。
The focus of this thesis is to investigate the relationship between the invariants, boundary conditions, and chiral edge states in Floquet topological systems. Using Floquet topological models on both honeycomb and T3 lattices, we calculate their invariants to predict the presence of chiral edge states. The band structures are simulated under various boundary conditions for each lattice, allowing us to observe whether the results align with the predictions of the invariants and to explore the similarities and differences in chiral edge states between different boundary conditions and lattice structures.
[1] Klitzing, K.v., G. Dorda, and M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett. 45, 494 (1980).
[2] Thouless, D.J., et al., Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405 (1982).
[3] DAI Xi, Topological phases and transitions in condensed matter systems, 物理 · 45卷 (2016 年) 12 期。
[4] 蔡雅雯、吳杰倫、欒丕綱, 從量子霍爾效應到拓樸光子學與拓樸聲子學, 科儀新知 211 期, 68 (2017)。
[5] Haldane, F.D.M., Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the" parity anomaly", Phys. Rev. Lett. 61,
2015 (1988).
[6] C.L. Kane, and E.J. Mele, Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005).
[7] C. L. Kane and E. J. Mele, Z2 Topological Order and the Quantum Spin Hall Effect, Phys. Rev. Lett. 95, 146802 (2005).
[8] P. M. Perez-Piskunow, Gonzalo Usaj, C. A. Balseiro, and L. E. F. Foa Torres, Floquet chiral edge states in graphene, Phys. Rev. B 89, 121401(R) (2014).
[9] Gonzalo Usaj, P. M. Perez-Piskunow, L. E. F. Foa Torres, and C. A. Balseiro, Irradiated graphene as a tunable Floquet topological insulator, Phys. Rev. B 90, 115423 (2014).
[10] Konrad Viebahn, Introduction to Floquet theory, Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland (2020).
[11] Takashi Oka, and Sota Kitamura, Floquet Engineering of Quantum Materials, Annu. Rev. Condens. Matter Phys. 10, 387-408 (2019).
[12] Mark S. Rudner, Netanel H. Lindner, The Floquet Engineer's Handbook, arXiv:2003.08252v2.
[13] Mark S. Rudner, Netanel H. Lindner, Erez Berg, and Michael Levin, Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems, Phys. Rev. X 3, 031005 (2013).
[14] Longwen Zhou and Jiangbin Gong, Recipe for creating an arbitrary number of Floquet chiral edge states, Phys. Rev. B 97, 245430 (2018).
[15] Yang, Z., Lustig, E., Lumer, Y. et al. Photonic Floquet topological insulators in a fractal lattice. Light Sci Appl 9, 128 (2020).
[16] Kitamura, S., Aoki, H. Floquet topological superconductivity induced by chiral many-body interaction. Commun Phys 5, 174 (2022).
[17] M. V. Berry, Quantal Phase Factors Accompanying Adiabatic Changes, Proc. R. Soc. Lond. A 392, 45-57 (1984).
[18] Hai-Xiao Wang, Guang-Yu Guo and Jian-Hua Jiang, Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology, New J. Phys. 21 (2019) 093029.
[19] R. Bott and R. Seeley, Some remarks on the paper of callias, Commun. Math. Phys. 62, 235 (1978).
[20] Muhammad Umer, Raditya Weda Bomantara, and Jiangbin Gong, Counterpropagating edge states in Floquet topological insulating phases, Phys. Rev. B 101, 235438 (2020).
[21] Takuya Kitagawa, Erez Berg, Mark Rudner, and Eugene Demler, Topological characterization of periodically driven quantum systems, Phys. Rev. B 82, 235114 (2010).
[22] I. C. Fulga and M. Maksymenko, Scattering matrix invariants of Floquet topological insulators, Phys. Rev. B 93, 075405 (2016).
[23] Mahito Kohmoto1 and Yasumasa Hasegawa, Zero modes and edge states of the honeycomb lattice, Phys. Rev. B 76, 205402 (2007).
[24] Bashab Dey and Tarun Kanti Ghosh, Floquet topological phase transition in the lattice, Phys. Rev. B 99, 205429 (2019).
