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研究生： 楊柏源
Yang, Po-Yuan
論文名稱： 探索二維外爾半金屬的拓樸相變以及奇偶性異常
Investigation of Topological Phase Transition and Parity Anomaly in Two-Dimensional Weyl Semimetal
指導教授： 張泰榕
Chang, Tay-Rong
學位類別： 碩士
Master
系所名稱： 理學院 - 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： 73
中文關鍵詞： 二維外爾半金屬 、佛凱定理 、奇偶性異常
外文關鍵詞： 2d Weyl semimetal, Parity anomlay
相關次數： 點閱：77  下載：16 
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    • 外爾半金屬為拓樸材料家族中的一員，它具有獨特的電子結構，包括帶有自旋極化的線性狄拉克能帶以及在材料表面形成的費米弧。這些材料由於在電子、光學和自旋電子學等領域的潛在應用而引起了相當的關注。三維的外爾材料已被人們熟知，但二維的外爾材料還未被人們了解。外爾半金屬中的最後的一塊拼圖由我們這次的工作補全。本篇論文將聚焦於二維外爾半金屬的拓樸性質計算以及光學響應。我們發現利用硒化錫基板破壞單層鉍的空間返演對稱，能使單層鉍的能帶結構變為一般絕緣體，並且在相變線上出現二維外爾態。接著，我們應用佛凱微擾理論來探討光場誘導的拓樸相變。我們發現單層鉍的其中一個外爾點在佛凱微擾作用下打開能隙，使得單層鉍僅存在單個外爾能錐。此外，我們的計算顯示該拓樸態具有罕見的半整數的量子化爾電導。該效應是由於U(1)對稱破壞所產生，對應高能物理中的「奇偶異常(Parity anomaly)」。因此，我們的工作不只實現了二維外爾半金屬，更提供了在凝態系統中研究奇偶異常此基礎物理定律的良好平台。

    Two-dimensional Weyl semimetal are recently discovered novel materials. In this paper, we primarily investigate their response to special light fields. We observe that under the influence of a light field, this material exhibits the phenomenon of "parity anomaly." This paper show the complete phase transition process and the half-integer anomalous Hall conductivity. The tools employed in this study include "Density Functional Theory, Semi-infinite Method, Floquet Engineering, Berryology, Kubo Formula,etc".

    Contents 摘要 i 英文摘要 ii 目錄 xi 圖目錄 xiv 第1章Introduction 1 1.1 Purpose of study 1 1.2 Organization of thesis 2 第2章週期性晶格和Bloch’s theory 3 2.1 Bloch’s theroem 3 2.2 Tight-binding Method 5 2.2.1 Wannier function 6 2.3 Density functional theory 6 第3章Berryology 的介紹和計算方法 8 3.1 Berry phase 8 3.1.1 Adiabatic theorm 9 3.1.2 Berry connection 10 3.1.3 Berry curvature、Berry flux 12 3.2 Berryology 和週期性晶格15 3.2.1 Berryology 在一維週期性晶格 15 3.2.2 Berryology 在二維週期性晶格 17 3.3 Quantum Anomalous Hall Conductivity 19 第4章Haldane’s Model 20 4.1 Graphene model 20 4.2 Make Graphene topology 22 4.2.1 Break inversion symmetry 23 4.2.2 Break time reversal symmetry 23 4.3 Berryology of Haldane Model 25 4.3.1 Edge States 26 4.4 Quantum anomalous Hall effect in Haldane’s model 28 第5章Dirac semimetal and Weyl semimetal 29 5.1 2D-Dirac/Weyl semimetal 30 5.1.1 Without Spin-Orbital Coupling 30 5.1.2 With Spin-Orbital Coulping 32 5.1.3 Tight binding Model for 2d-Weyl semimetal 32 5.2 First principle calculation for 2d-Weyl semimetal 35 5.2.1 Epitaxial Bismuthene on SnSe 之原子結構 35 5.2.2 Epitaxial Bismuthene on SnSe 之電子結構 36 5.2.3 Semi-infinite Epitaxial Bismuthene on SnSe 37 5.3 Spin Hall conductivity Calculation 40 第6章Floquet engineering 計算方法 41 6.1 Quantum Floquet theory 41 6.2 Effective Hamiltonian and High-frequency expansion 45 第7章Photoinduced Hamiltonian of 2D-Weyl semimetal 47 7.1 Floquet Perturbation in Epitaxial Bismuthene on SnSe 47 7.1.1 Phase transition in 2d-Weyl semimetal State 48 7.1.2 Phase transition in Trivial insulator State 50 7.1.3 Phase transition in Quantum spin Hall State 52 7.2 Quantum anomalous Hall effect in Epitaxial Bismuthene on SnSe 54 7.3 Why there are single Dirac cone and half-integer conductivity 55 7.4 Parity anomaly in Epitaxial Bismuthene on SnSe 56 第8章Conclusion 58 Appendix A:Semi-infinite method 60 Appendix B:Linear Respond Theory 62 Appendix C:Spin Hall conductivity Calculation 69 References 70

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