力學蜂窩晶格之拓樸邊緣態探討

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姓名

翁榮恩(Rong-En Weng) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

力學蜂窩晶格之拓樸邊緣態探討
(Study on the topological edge states of mechanical honeycomb lattice)

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摘要(中)

本論文首先探討力學蜂窩晶格於幾類邊界條件下的邊緣態，對其存在緣由作出解釋。隨後引入科氏力破壞時間反演對稱以產生手徵邊緣態，並檢視與此相關的拓樸相變。再者考察晶格錯位時邊緣態與缺陷態的耦合情形，藉以比較各類邊緣態對晶格錯位之容忍度。最後引入次近鄰連結，探討因歪折邊界連結角度而產生的邊緣態。

摘要(英)

In this thesis we first discuss the edge states of the mechanical honeycomb lattice under several types of boundary conditions, and explain the underlying mechanisms of their existence. Subsequently, Coriolis force is introduced to break the time reversal symmetry and generate chiral edge states. The corresponding topological phase transition is also examined. Furthermore, the coupling of edge states and defect states under lattice dislocation is investigated, so as to compare the tolerance of various edge states to lattice dislocation. Finally, the next-nearest-neighbor connection is considered, so as to discuss the edge states caused by distorting the angle of the boundary connections.

關鍵字(中)

★ 拓樸邊緣態

關鍵字(英)

論文目次

目錄
摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 V
第一章緒論 1
第二章理論與算法 6
2-1 陳數與威爾森迴圈算法 6
2-2 時間反演算子與平移不變系統 10
2-3 邊緣態與體系—邊界對應 11
第三章力學蜂窩晶格模型 15
3-1 運動方程 15
3-2 單向有界能帶結構 18
3-3 無界能帶結構 20
3-4 陳數計算程序 21
第四章數值結果與討論 23
4-1 蜂窩晶格體帶與邊緣態 23
4-1-1 Ω=0 時的邊緣態探討 24
4-1-2 Ω≠0 時的邊緣態探討 30
4-1-3 晶格錯位對邊緣態之影響 36
4-2 次近鄰連結蜂窩晶格 40
4-2-2 Ω=0 時的邊緣態探討 40
4-2-2 Ω≠0 時的邊緣態探討 42
第五章結論與未來展望 44
5-1 結論 44
5-2 未來展望 44
參考文獻 46

參考文獻

參考文獻

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指導教授

欒丕綱

審核日期

2021-5-25

推文