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研究生： 姚有徽
Io, Iao-Fai
論文名稱： 一維non-Hermitian 拓樸模型
1D non-Hermitian topological model
指導教授： 高賢忠
Kao, Hsien-Chung
口試委員： 高賢忠
Kao, Hsien-Chung
游至仕
You, Jhih-Shih
謝長澤
Hsieh, Chang-Tse
口試日期： 2022/06/22
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2022
畢業學年度： 110
語文別： 中文
論文頁數： 58
中文關鍵詞： SSH Model 、bulk-edge correspondence 、Non-Hermitian 、Exceptional point
英文關鍵詞： SSH Model, bulk-edge correspondence, Non-Hermitian, Exceptional point
研究方法: 主題分析
DOI URL： http://doi.org/10.6345/NTNU202200825
論文種類： 學術論文
相關次數： 點閱：65  下載：21 
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    • 本文首先介紹在一維拓樸絕緣體常討論的Su-Schrieffer-Heeger (SSH) model以及其推廣的模型，我們可以用bulk-edge correspondence去預測拓樸系統中邊界態數目。接下來將上述的模型推廣到non-Hermitian (NH)的形式，我們發現在NH系統中存在skin effect以及exceptional point，這些是當系統為Hermitian時不具有的性質。我們利用解析解計算研究exceptional points (EPs)在不同的模型下出現的條件，並了解其性質。

    In this thesis we will introduce the Su-Schrieffer-Heeger (SSH) model, which is a prototype of one dimension topological insulator and its extended versions. It is known that bulk-edge correspondence may be used to predict the number of edge state on the boundary of a topological system. Next we extended these models to non-Hermitian (NH) Form, we found that in a NH system there exists skin effect and exceptional points which cannot be found in a Hermitian system. We use analytical calculation to find the condition of exceptional points (EPs) in different models, and study their property.

    摘要 ii Abstract iii Content iv Chapter 1 Hermitian topological model 1 1.1 Su-Schrieffer-Heeger model 1 1.1.1 Odd number particle SSH model 2 1.1.2 Even number particle SSH model 4 1.2 Bulk-edge correspondence 7 1.2.1 Berry phase 7 1.2.2 Winding number 8 1.2.3 Application in SSH model 8 1.3 Extended SSH model 10 1.3.1 Type A extended SSH model 10 1.3.2 Type B extended SSH model 13 1.3.3 Odd number particle extended SSH model 17 Chapter 2 Non-Hermitian topological model 23 2.1 Non-Hermitian Su-Schrieffer-Heeger model 23 2.1.1 Odd number particle NH SSH model 24 2.1.2 Even number particle NH SSH model 27 2.2 Bulk-edge correspondence 28 2.2.1 Non-Hermitian Berry phase and winding number 28 2.2.2 Application in NH SSH model 29 2.3 Non-Hermitian extended SSH model 31 2.3.1 Type A NH extended SSH model 31 2.3.2 Type B NH extended SSH model 36 2.3.3 Odd number particle NH extended SSH model 39 Chapter 3 Edge state exceptional point 43 3.1 Special property in non-Hermitian system 43 3.1.1 Exceptional points (EPs) 43 3.1.2 Jordan block decomposition 43 3.1.3 Zero hopping in NH SSH model 45 3.2 Exceptional points in type B NH extended SSH model 47 3.2.1 Numerical result of edge state energy 47 3.2.2 Exceptional points condition 48 3.3 Exceptional points in odd number particle NH extended SSH model 52 3.3.1 Numerical result of edge state energy 52 3.3.2 Exceptional points condition 53 Chapter 4 Conclusion 57 Reference 58

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