我們利用第一原理電子結構計算預測新一類的二維 (2D) 拓撲絕緣體 (TIs) 基於氫化的錫薄膜。單一雙分子層 (bilayer) 錫薄膜 (stanene) 已經被確定為一個二維拓撲絕緣體。而將其雙面鍵結氫原子後，會從拓撲態轉變成一般態。根據我們的宇稱 (parity) 分析，錫烯 (stanene) 的兩層和三層雙分子層為一般態。此外，錫烷 (stanane) 兩層、三層和四層雙分子層是拓撲態。對高達三層雙分子層厚度錫薄膜雙面鍵結氫原子鈍化時，會從金屬變成絕緣體。最後，對碘鈍化 (iodine-terminated) 的錫薄膜沿著對角線 (111) 方向高達三層雙分子層進行了研究，發現皆為拓撲態，並且該系統兩層雙分子層以上為半金屬。與具有340 meV 能隙的單一雙分子層碘鈍化錫薄膜比較有很大的差距。因此，碘鈍化不能相同應用在兩層、三層雙分子層錫薄膜上。

We use first-principles electronic structure calculations to predict a new class of two-dimensional (2D) topological insulators (TIs) in hydrogenated ultra-thin tin films. Single bilayer tin film had been identified as a two-dimensional topological insulator and it transforms into a trivial insulator after hydrogenation. Based on our parity analysis, tin films with two and three bilayers are in trivial phase. In addition, hydrogenated tin films with two, three and four bilayers are non-trivial. For the thickness of tin films up to three bilayers, the tin films were altered from metallic to insulating after H-passivations. Finally, the iodine-terminated tin films up to three bilayers were also studied and they all are found to be non-trivial. The systems become semi-metallic beyond single bilayer. Thus, a large gap of 340 meV for single iodine-terminated bilayer can not be replicated in iodine-terminated two- and three-bilayer tin films.

論文審定書 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 v
表次 ix
1. 緒論： 1
2. 理論與方法： 3
2.1密度泛函理論 (DFT) 3
2.2贗位勢方法 10
2.3海爾曼-費曼理論 14
2.4拓撲絕緣體 15
2.5計算方法 18
3.結果與討論：四族(111)面薄膜 19
3.1四族(111)面薄膜之原子結構 19
3.2四族(111)面薄膜之能帶圖 24
3.3四族(111)面薄膜之宇稱分析 33
4.結果與討論：錫烯與錫烷 36
4.1錫烯與錫烷多層之原子結構 36
4.2應力引起錫烯與錫烷多層之拓撲相變 39
4.3碘鈍化之錫(111)面薄膜多層拓撲性質 51
5.結論： 53
參考文獻 54

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