近年來，拓樸絕緣體備受關注，其為一種特殊材料，內部不導電，但在結構表面或介面處可允許電流通過。透過量子霍爾效應，可類比至聲子晶體。藉由改變結構對稱性或施加外部場，打破空間或時間反演對稱，使材料色散曲線中的狄拉克點被拉開並產生拓樸相變，便可利用邊緣模態控制波的傳遞方向。
本文設計樑中間嵌入散射柱組成單位晶胞，接著改變其結構的對稱性，同時導入量子能谷霍爾效應，研究彈性波於固體材料中的波傳現象。首先，建立結構模型，利用有限元素法商業軟體 COMSOL Multiphysics® 計算出其能帶結構，並設計材料性質與結構參數找出狄拉克點，並討論改變結構參數對於狄拉克點的影響。接著改變散射柱離晶格中心距離拉開狄拉克點並討論模態反轉現象。接著利用超晶胞法分析兩種拓樸不等價聲子晶體所組成的介面並於邊體關係圖尋找能量集中於介面處之邊緣模態。最後，於結構中激發於邊緣模態頻率範圍之彈性波，進而驗證其特殊波傳行為。
分別討論四種不同形狀之散射柱，利用超晶胞法找出各自邊緣模態頻率範圍，並設計直線及Z字形全波模擬結構，這兩種全波模擬結構個別包含三種路徑：完美介面、亂序、缺陷。藉由比較三種路徑及Z字形結構的彎角路徑驗證邊緣模態對於抑制後向散射及缺陷免疫的穩健性，並參考位移穿透頻譜圖確認其高傳輸性質。利用具有拓樸性質之聲子晶體，將可應用於設計彈性波波導或是獵能器等裝置。

In the present study, a two-dimensional phononic crystal with quantum valley Hall effect is proposed to exhibit the topologically protected edge mode in elastic wave, which only occurs at the interface between two topologically inequivalent phononic crystals. The unit cell of the topologically phononic crystal is composed of the scattering pillars embedded in the middle of the beam, and the Dirac point at the K-point in the irreducible Brillouin zone is investigated. Also, two topological inequivalent phononic crystals are obtained by breaking the spatial inversion symmetry of the primitive cell, and then study the edge mode at the interface by the supercell method and the full-wave simulation by the finite element analysis software COMSOL Multiphysics®. The robustness of edge mode for limiting the backscattering and defect immunity is perfectly verified. Our study may offer a brand new application in high-efficiency waveguide and energy harvesting devices.

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