博碩士論文 111226009 詳細資訊




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姓名 邱義軒(Yi-Hsuan Chiu)  查詢紙本館藏   畢業系所 光電科學與工程學系
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)
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ T3晶格
★ 弗洛凱拓樸
★ 弗洛凱拓樸邊緣態
★ T3弗洛凱拓樸
關鍵字(英) ★ T_3 lattice
★ Floquet topological
★ Floquet topological edge states
★ T_3 Floquet topological
論文目次 摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 V
第一章、緒論 1
1.1拓樸絕緣體 1
1.2週期驅動弗洛凱 (Floquet) 拓樸絕緣體 3
1.3 本文架構 5
第二章、研究理論 6
2.1 弗洛凱(Floquet)理論 6
2.2 貝里相 (Berry phase)、陳數 (Chern number) 和威爾森迴圈 (Wilson loop) 9
2.4 卷繞數 (winding number) 12
第三章、蜂窩晶格弗洛凱拓樸模型 16
3.1 蜂窩晶格 (honeycomb lattice) 模型 16
3.2週期淬火 (quench) 調制蜂窩晶格 18
3.3 拓樸不變量的計算 22
3.4 手性邊緣態的模擬 24
第四章、T_3晶格弗洛凱拓樸模型 29
4.1 T_3 晶格模型 29
4.2 週期淬火 (quench) 調制T_3晶格 32
4.3 T_3晶格拓樸不變量的計算 34
4.4 T_3 晶格手性邊緣態的模擬 36
4.4.1之字形 zigzag 和鬍鬚 beard邊界 36
4.4.2 扶手椅 (armchair) 邊界 40
第五章、結論與未來展望 43
5.1 結論 43
5.2未來展望 44
參考資料 45
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指導教授 欒丕綱(Pi-Gang Luan) 審核日期 2025-1-20
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