本研究利用第一原理方法預測鉈和五族化合物的塊材和薄膜為拓撲絕緣體材料 (topological , TIs)。藉由計算拓撲不變量(Z2)，我們確認了鉍化鉈 (TlBi) 的塊材為弱拓撲絕緣體 (weak topological insulator) 的半金屬，除此之外，磷化鉈 (TlP) 和砷化鉈 (TlAs) 在受到非均向單軸應變 (uniaxial strain) 後，會變為強拓撲絕緣體 (strong topological insulator) 的絕緣體或半金屬。關於二維薄膜，我們發現雙層雙分子層的砷化鉈 (TlAs) 和銻化鉈 (TlSb) 於懸空 (free standing) 或是與氫鍵結時皆為拓撲態，且他們可以承受大幅度的應變仍保持拓撲態。另外，氮化鉈 (TlN) 和磷化鉈 (TlP) 雖然在平衡態時為一般態，但仍可藉由適度的應力而變為拓撲態。所有的二維薄膜的能隙都小於80毫電子伏特，而在室溫之下應用仍待進一步的研究。

We used first-principles electronic structure calculations to predict topological properties in binary compositions of Thallium (Tl) and group V elements in bulks and thin films. Determined by the calculated the topological invariants (Z2), we identified bulk TlBi is a weak topological insulator (TI) and a semimetal. Furthermore, bulk TlP and TlAs are metals and become topological insulator and then semimetal under external strain. As for two-dimensional thin films, we found nontrivial TI phase in two bilayers of hydrogenated TlAs and TlSb, which can withstand a wide range of strain. Additionally, TlN and TlBi could still be driven to nontrivial phase at some strain values. We note energy gaps of all the two-dimensional thin files generally less than 80 meV. Their application at room temperature is pending further studies.

論文審定書 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 vi
表次 viii
1.緒論 1
2.理論與計算方法 3
2.1拓撲絕緣體 3
2.1.1 拓撲不變量 3
2.1.2 從能帶結構判斷拓撲性質 4
2.2 計算方法 5
3. 結果與討論:鉈和五族化合物之塊材 6
3.1 鉈和五族化合物之結構預測和能帶結構 6
3.2 磷化鉈和砷化鉈應變效應 10
4. 結果與討論:鉈和五族化合物之薄膜 15
4.1  鉈和五族化合物之二層薄膜 15
4.2  鉈和五族化合物之二層氫鈍化薄膜 20
4.3  應變效應和拓撲相變 24
5. 結論 27
參考文獻 28

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