我們利用第一原理計算研究雙面分別與氫和氮鍵結之蜂巢狀鍺烯的原子結構
與電子特性。在原子結構上可分為三種：平面、皺摺和反皺摺蜂巢結構。我們發
現，反皺摺結構擁有相對穩定的無磁性絕緣體；同時皺摺結構則為金屬性材料。
在晶格常數 4.00 埃的平面結構下使用自旋極化計算並包含自璇軌道耦合後，可
發現量子異常霍爾絕緣體。為了驗證材料的拓撲性，進一步計算陳數與邊界態。
並且在鋸齒形帶狀結構邊界態的能帶結構中發現一條連接導帶與價帶的能帶。我
們的結果顯示，官能化之鍺烯能被用於備受追尋的自旋電子應用。

We study the atomic structures and electronic properties of honeycomb germanene
passivated with hydrogen and nitrogen (GeHN) atoms using first-principles electronic
structure calculations. There are three atomic structures considered: planar, buckled, and
inversely buckled honeycomb. We found that the inversely buckled structure is relatively
stable with non-magnetic insulator phase; while the buckled structure is metallic. Using
spin-polarized calculations with spin-orbit coupling, GeHN in planar structure with lattice
constant at a=4.00 Å was identified to exhibit a quantum anomalous Hall (QAH) insulator
phase. In order to confirm the topology of the material, we further calculated the Chern
number as well as the edge states. A band connecting the conduction and the valence band
was found at the edge state of zigzag GeHN nanoribbon. Our results suggest that
functionalized germanene could be used in the highly sought spintronic applications
based on QAH effect.

論文審定書…………………………………………………………………… i
中文摘要……………………………………………………………………… ii
英文摘要……………………………………………………………………… iii
第 一 章 序論與動機……………………………………………………… 1
1.1 緒論…………………………………………………………… 1
1.2 動機…………………………………………………………… 3
第 二 章 研究方法………………………………………………………… 4
2.1 第一原理……………………………………………………… 4
2.2 貝瑞曲率……………………………………………………… 5
2.3 陳數…………………………………………………………… 7
2.4 量子異常霍爾效應…………………………………………… 7
第 三 章 結果與討論……………………………………………………… 9
3.1 雙面分別與氫和氮鍵結之鍺烯的結構……………………… 9
3.2 鍺烯在不同晶格常數下的穩定性研究……………………… 10
3.3 應力引起雙面分別與氫和氮鍵結之鍺烯的能帶結構變化… 13
3.4 應力引發之磁性與能帶結構的細節變化…………………… 16
3.5 初始磁動量對能帶的影響…………………………………… 18
3.6 自旋軌道耦合對能帶的影響………………………………… 21
3.7 貝瑞曲率，陳數與邊界態…………………………………… 22
第 四 章 總結…………………………………………………………… 26
參考資料……………………………………………………………………… 27

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