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研究生： 郭佩茹
Guo, Pei-Ju
論文名稱： 阿基米德晶格聲子晶體拓樸能谷邊緣態之研究
The topological valley edge state of the Archimedean tilings phononic crystal
指導教授： 陳聯文
Chen, Lien-Wen
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 114
中文關鍵詞： 聲子晶體 、阿基米德晶格 、拓樸絕緣體
外文關鍵詞： topological insulators, quantum valley Hall effect, Archimedean tilings
相關次數： 點閱：49  下載：2 
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    • 絕緣體因不存在自由電子，因此無法藉由電子的流動而導電。拓樸絕緣體卻有著強大的傳輸行為，因此在許多領域上備受矚目。拓樸絕緣體為一固體材料，其內部絕緣，但表面存在特殊的量子態而允許電荷傳輸。拓樸絕緣體基於量子霍爾效應、量子自旋霍爾效應以及量子能谷霍爾效應等理論，在電磁波、聲波、彈性波等領域都有許多學者進行研究。
    阿基米德晶格結構為一種具有高度對稱性之結構，此晶格結構是使用一種或一種以上的正多邊形所編織成整個平面的晶格，並且每個多邊形都互相緊密連接，沒有產生縫隙或重疊部分。
    本文選定Archimedean(3,4,6,4)晶格聲子晶體，在縱波/聲波下基於量子能谷霍爾效應之理論，利用有限元素法軟體，求得其能帶結構。再藉由改變晶格結構破壞空間反演對稱性，探討拓樸不等價之結構。並設計不同界面及傳輸路徑，驗證所設計之結構具有高穿透率且可忽略缺陷及後向散射等強大的波傳特性。

    Recent years, the researches of topological insulators(ITs) have been involved in bunches of distinct fields, such as electromagnetic wave, sound waves, and elastic wave, etc. In this thesis, we present a study of ITs on longitudinal wave and sound wave based on quantum valley Hall effect(QVHE) theory with Archimedean(3,4,6,4) tilings phononic crystal. We destroyed the spatial inversion symmetry by changing the lattice parameters. Then we can get two inequivalent structures. Next, we used the two inequivalent structures to design five paths of propagation which are perfect, Z-shape, disorder, defect 1 and defect 2. Through two topologically distinct interfaces, we prove our structures possess not only high transmission but strong wave propagation which can neglect defects and immune backscattering.

    中英文摘要 I 誌謝 XV 目錄 XVI 表目錄 XIX 圖目錄 XX 符號 XXVI 第一章 緒論 1 1.1. 前言 1 1.2. 文獻回顧 2 1.2.1. 聲子晶體 2 1.2.2. 聲子晶體之能隙現象 2 1.2.3. 阿基米德晶格 3 1.2.4. 拓樸學與量子霍爾效應 4 1.2.5. 量子自旋霍爾效應與量子能谷霍爾效應 4 1.2.6. 拓樸絕緣體 5 1.3. 本文架構 6 第二章 理論與數值方法 10 2.1. 前言 10 2.2. 固態物理學之基本定義 10 2.2.1. 實晶與倒晶格(Reciprocal Lattice) 10 2.2.2. 布里淵區(Brillouin Zones)與布洛赫定理(Bloch theorem) 11 2.3. 有限元素法 13 2.4. 拓樸學(Topology) 16 2.4.1. 能帶理論(Band Theory)與拓樸 16 2.4.2. 貝里相位與陳數 17 2.5. 量子霍爾效應簡介 18 2.5.1. 整數量子霍爾效應 18 2.5.2. 量子自旋霍爾效應 19 2.5.3. 量子能谷霍爾效應 19 第三章 探討縱波對於阿基米德結構拓樸效應 26 3.1. 前言 26 3.2. 阿基米德結構幾何模型與能帶分析 26 3.2.1. 阿基米德結構模型建立 26 3.2.2. 阿基米德結構能帶分析 26 3.2.3. 改變幾何參數對能帶結構之分析 27 3.2.4. 改變幾何參數之拓樸相變 27 3.3. 邊體關係圖(Edge-Bulk Correspondence) 28 3.3.1. 超晶胞(Supercell)法與界面型態 28 3.3.2. 邊緣模態與邊體關係圖(Edge-Bulk Correspondence)分析 28 3.4. 全波模擬(Full wave simulation)分析 29 3.4.1. 參數f=±0.1時I-II型界面全波模擬 29 3.4.2. 參數f=±0.1時II-I型界面全波模擬 31 3.4.3. 參數f=±0.2時I-II型界面全波模擬 31 3.4.4. 參數f=±0.2時II-I型界面全波模擬 32 第四章 探討聲波對於阿基米德結構拓樸效應 58 4.1. 前言 58 4.2. 阿基米德結構幾何模型與能帶分析 58 4.2.1. 阿基米德結構模型建立 58 4.2.2. 阿基米德結構能帶分析 58 4.2.3. 改變幾何參數對能帶結構之分析 58 4.2.4. 改變幾何參數之拓樸相變 59 4.3. 邊體關係圖(Edge-Bulk Correspondence) 59 4.3.1. 超晶胞(Supercell)法與界面型態 59 4.3.2. Straight界面邊體關係圖分析 60 4.3.3. Zigzag界面邊體關係圖分析 61 4.4. Straight界面全波模擬(Full wave simulation)分析 61 4.4.1. Straight界面參數f=±0.1時I-II型全波模擬 62 4.4.2. Straight界面參數f=±0.1時II-I型全波模擬 63 4.4.3. Straight界面參數f=±0.2時I-II型全波模擬 63 4.4.4. Straight界面參數f=±0.2時II-I型全波模擬 64 4.5. Zigzag界面全波模擬(Full wave simulation)分析 65 4.5.1. Zigzag界面參數f=±0.1時I-II型全波模擬 65 4.5.2. Zigzag界面參數f=±0.1時II-I型全波模擬 66 4.5.3. Zigzag界面參數f=±0.2時I-II型全波模擬 66 4.5.4. Zigzag界面參數f=±0.2時II-I型全波模擬 67 第五章 綜合討論與未來展望 108 5.1. 綜合結論 108 5.2. 未來展望 109 參考文獻 110

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