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研究生: 黃正源
Huang, Cheng-Yuan
論文名稱: 具有一般邊界條件的Non-Hermitian SSH模型
Non-Hermitian SSH Model with General Boundary Condition
指導教授: 高賢忠
Kao, Hsien-Chung
口試委員: 謝長澤
Hsieh, Chang-Tse
游至仕
You, Jhih-Shih
高賢忠
Kao, Hsien-chung
口試日期: 2023/01/03
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 48
英文關鍵詞: SSH model, bulk edge correspondencce, non-Hermitian SSH model, exceptional points
DOI URL: http://doi.org/10.6345/NTNU202300045
論文種類: 學術論文
相關次數: 點閱:93下載:13
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  • 本文主要研究滿足一般邊界條界的Non-Hermitian Su-Schrieffer-Heeger (nSSH)模型。我首先介紹Su-Schrieffer-Heeger (SSH)模型,透過bulk edge correspondence來預測該系統邊界態的數目。接著將這些想法推廣至non-Hermitian的系統,並且介紹更一般的邊界條件。我發現不同於SSH模型,此時系統存在skin effect及exceptional points。並且列出exceptional points出現的條件,討論其中有趣的性質。

    abstract ii 1 A Brief Introduction to the Hermitian SSH Model 1 1.1 Hermitian SSH Model with Open Boundary Condition . . . . . . . . 1 1.2 Hermitian SSH Model with Periodic Boundary Condition . . . . . . . 6 1.3 Bulk Edge Correspondence in SSH Model . . . . . . . . . . . . . . . . 8 2 Non-Hermitian SSH Model 13 2.1 Non-Hermitian SSH Model with Open Boundary Condition . . . . . . 13 2.2 Non-Hermitian SSH Model with Periodic Boundary Condition . . . . 18 2.3 Bulk Edge Correspondence in non-Hermitian SSH Model . . . . . . . 20 3 Non-Hermitian SSH Model with General Boundary Condition 23 3.1 Standard Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Some Interesting Limit . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 Exceptional Points and Jordan Block Decomposition 37 4.1 Exceptional Points and Jordan Decomposition in Non-Hermitian System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Applications in Non-Hermitian SSH Model . . . . . . . . . . . . . . . 39 4.3 Singular Limits of the Non-Hermitian SSH Model . . . . . . . . . . . 40 5 Conclusion 46 References 47

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