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。
Asbóth, János K. and Oroszlány, László and Pályi, András, "A Short Course on Topological Insulators:Band Structure and Edge States in One and Two Dimensions," 978-3-319-25605-4 Springer Published: 23 February 2016.
Chen, Ze-Guo and Wang, Licheng and Zhang, Guanqing and Ma, Guancong, "Chiral Symmetry Breaking of Tight-Binding Models in Coupled Acoustic-Cavity Systems," Phys. Rev. Appl. 14, 024023 (2020).
Xueda Wen and Marvin Qi and Agnès Beaudry and Juan Moreno and Markus J. Pflaum and Daniel Spiegel and Ashvin Vishwanath and Michael Hermele, "Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems," arXiv:2112.07748 (2021).
Maxim Braverman, "The Berry phase and the phase of the determinant," J. Math. Phys. 55, 042106 (2014).
Marcos Atala, Monika Aidelsburger, Julio T. Barreiro, Dmitry Abanin, Takuya Kitagawa, Eugene Demler, and Immanuel Bloch, "Direct measurement of the Zak phase in topological Bloch bands," Nat. Phys. 9, 795 (2013).
Han-Ting Chen and Chia-Hsun Chang and Hsien-chung Kao, "Connection between the winding number and the Chern number," Chinese J. Phys. 72, 50 ( 2021).
Lieu, Simon, "Topological phases in the non-Hermitian Su-Schrieffer-Heeger model," Phys. Rev. B 97, 045106 (2018).
Bender, Carl M. and Mannheim, Philip D., "Exactly solvablePT-symmetric Hamiltonian having no Hermitian counterpart," Phys. Rev. D 78, 025022 (2008).
Stefano Longhi, "Non-Hermitian skin effect beyond the tight-binding models," Phys. Rev. B 104, 125109 (2021).
Y. Z. Han, J. S. Liu, and C. S. Liu, "The topological counterparts of non-Hermitian SSH models," New J. Phys. 23, 123029 (2021).
Kunst, Flore K. and Edvardsson, Elisabet and Budich, Jan Carl and Bergholtz, Emil J., "Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems," Phys. Rev. Lett. 121, 026808 (2018).
Rebekka Koch, and Jan Carl Budich, "Bulk-boundary correspondence in non-Hermitian systems:
stability analysis for generalized boundary conditions," Eur. Phys. J. D 74, 70 (2020).
Bergholtz, Emil J. and Budich, Jan Carl and Kunst, Flore K., "Exceptional topology of non-Hermitian systems," Rev. Mod. Phys. 93, 015005 (2021).
Gene H. Golub and James Hardy Wilkinson, "Ill-conditioned eigensystems and the computation of the Jordan canonical form," SIAM Review 18, 578 (1976).
Leykam, Daniel and Bliokh, Konstantin Y. and Huang, Chunli and Chong, Y.D. and Nori, Franco, "Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems," Phys. Rev. Lett. 118, 040401 (2017).
Wang, C. and Wang, X.-R. and Guo, C.-X. and Kou, S.-P., "Defective edge states and anomalous bulk-boundary correspondence for topological insulators under non-Hermitian similarity transformation," Int. J. Mod. Phys. B. 34, No. 09, 2050146 (2020).