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研究生： 翁榮恩
Rong-En Weng
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
指導教授： 欒丕綱
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： 2021
畢業學年度： 109
語文別： 中文
論文頁數： 57
中文關鍵詞： 拓樸邊緣態
相關次數： 點閱：9  下載：0 
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    • 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。

    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.

    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

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