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博碩士論文 etd-0802114-172916 詳細資訊
Title page for etd-0802114-172916
論文名稱
Title
三族鉍化物之寬能隙二維拓撲絕緣體理論預測
Prediction of large gap two-dimensional topological insulators consisting of bilayers of group III elements with Bi
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
54
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2014-05-29
繳交日期
Date of Submission
2014-09-02
關鍵字
Keywords
第一原理計算、電子結構、拓撲相變、量子霍爾效應、三五族半導體薄膜、二維拓撲絕緣體
Topological phase transition, First-principles calculations, Quantum spin Hall effect, 2D topological insulators, Electronic structures, III-V semiconductor thin films
統計
Statistics
本論文已被瀏覽 5672 次,被下載 863
The thesis/dissertation has been browsed 5672 times, has been downloaded 863 times.
中文摘要
本研究以第一原理方法對三族 (III A) 與鉍(Bi)之皺折蜂巢狀結構二元化合物做理論計算,並預測其為一類新的二維拓撲材料。同時在鉍化鎵(GaBi), 鉍化銦(InBi), 鉍化鉈(TlBi)三種化合物中發現能帶反轉的現象,其中最大之能隙為556毫電子伏特(meV), 此性質讓此類材料適合在室溫下應用。同時我們對針對技術上應用,針對材料的應變做出計算,發現鉍化硼(BBi), 鉍化鋁(AlBi)兩種材料在應變約6.6% 時會發生拓撲相變。而皺摺蜂巢狀的結構材料邊界上亦會有兩種不同類型的邊緣,鋸齒狀 (zigzag) 及扶手狀 (armchair),在後種邊界上,我們發現其在能帶結構上會有狄拉克錐 (Dirac cone) 般的能量色散關係,狄拉克點 (Dirac Point) 正好位於材料整體能隙的中間。能克服室溫的能隙加上狄拉克錐的能量色散關係是我們對於自旋傳輸機制一直以來的追求。本研究指出藉由適當的化學及力學調整,皺褶蜂巢狀結構對於產生非平庸 (nontrivial) 拓撲態及自旋極化的狄拉克費米(spin polarized Dirac fermions) 是一個適合的平台。
Abstract
We use first-principles electronic structure calculations to predict a new class of two-dimensional (2D) topological insulators (TIs) in binary compositions of group III elements (B, Al, Ga, In, and Tl) and bismuth (Bi) in a buckled honeycomb structure. We identify band inversions in pristine GaBi, InBi and TlBi bilayers, with gaps as large as 556 meV, making these materials appropriate suitable for room-temperature applications. Furthermore, we demonstrate the possibility of strain engineering in that the topological phase transition in BBi and AlBi could be driven at ~ 6.6% strain. The buckled structure allows the formation of two different topological edge states in the zigzag and armchair edges. More importantly, isolated Dirac-cone edge states are predicted for armchair edges with the Dirac point lying in the middle of the 2D bulk gap. Room-temperature bulk band gap and isolated Dirac cone allow these states to reach the long-sought topo-logical spin-transport regime. Our findings suggest that the buckled honeycomb struc-ture is a versatile platform for hosting nontrivial topological states and spin-polarized Dirac fermions with the flexibility of chemical and mechanical tunability.
目次 Table of Contents
論文審定書 i
摘要 ii
Abstract iii
圖次 vi
表次 vii
1. 導論 1
2. 理論與計算方法 3
2.1拓撲學背景 3
2.1.1 拓撲性質與空間聯絡 3
2.1.2 從能帶結構辨識拓撲絕緣體的方法 4
2.2 密度泛涵理論 (DFT) 5
2.2.1 湯瑪斯-費米 (Thomas-Fermi) 模型 5
2.2.2 霍恩貝格-柯恩 (Hohenberg-Kohn) 理論 6
2.2.3局域自旋密度近似(LSDA)與廣義梯度近似(GGA)下的柯恩-沈呂九(Kohn-Sham)方程式 8
2.2.4 自旋與軌道交互作用 11
2.3 贗位勢方法 13
2.3.1 範數守恆 (Norm-conserving) 之贗位勢 13
2.3.2 投影擴充平面波 (PAW) 15
2.4 赫爾曼-費曼(Hellmann-Feynman)理論 16
2.5 計算方法 17
3. 皺褶蜂巢狀結構三族鉍化物之結果 19
3.1皺褶蜂巢狀結構介紹 19
3.2 三族鉍化物(III-Bi)的能帶結構 24
3.3 邊緣態的能帶結構 30
3.4 應變效應與拓撲相變 35
3.5 拓撲金屬之邊緣態能帶結構 42
4. 結論 44
參考文獻 45
參考文獻 References
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