具大能隙的二維拓撲絕緣體，同時也被稱為量子自旋霍爾絕緣體，由於它自身自旋極化且具無背向散射的邊界傳導通道，對於低電耗的電子元件而言是被極度渴求的。雖然許多二維薄膜被預測為拓撲絕緣體，包括三族元素與鉍的獨立皺褶蜂巢結構，但是在實驗上尚未有二維量子自旋霍爾薄膜的證據。一般而言，二維薄膜的電子結構和能帶拓撲性質容易地受到基板的改變，使得了解二維拓撲絕緣體變成一種挑戰。我們從結合三族(硼、鋁、鎵、銦、鉈)和五族(氮、磷、砷、銻、鉍)元素25種化合物，未接氫的情況，另每一種化合物有兩種氫化方式共75種二維皺褶蜂巢結構中使用第一原理研究可能的量子自旋霍爾態，其中包含了結構單面與雙面吸附氫的狀態。氫化作用使材料增加能隙大小卻沒有改變能帶的拓撲性質。在三五族材料中，氫化的鉍化鉈能隙大小為885 meV，是適合在室溫中應用。而且鉍化鉈在不同氫濃度的吸附下依然保持大能隙的拓撲特性，即指出它的能帶拓撲性質是足以對抗大範圍的基板鍵結效應。

A large gap two-dimensional (2D) topological insulator (TI), also known as quantum spin Hall (QSH) insulator, is highly desired for low-power-consumption electronic devices, owing to its spin-polarized back-scattering-free edge conducting channels.
While many 2D thin films have been predicted as TIs, including free-standing buckled honeycomb with group III and Bi elements, there has been no evidence for 2D QSH thin films from the transport experiments.
In general, the electronic structures as well as the band topology of 2D thin films can be easily altered by substrates, making the materials realization of 2D TI quite a challenge.
We have carried out a first-principles study of possible quantum spin Hall (QSH) phases in 75 buckled honeycombs combining group III (B, Al, Ga, In, and Tl) and group V (N, P, As, Sb, and Bi) elements in the 2D buckled honeycomb structure, including effects of hydrogenation on one or both sides of the films to simulate the effect of substrate. Three unhydrogenated new compounds (TlAs, TlSb, and TlN) are identified to be nontrivial. Hydrogenation is shown to enhance the band gap without changing the band topology. The band gap is found to be as large as 855 meV for the hydrogenated TlBi case, making this class of III-V materials suitable for room temperature applications. Moreover, TlBi remains topologically nontrivial with a large band gap at various hydrogen coverages, indicating that its band topology is robust against bonding effects for a wide range of substrates.

論文審定書 i
Acknowledgements ii
摘要 iii
ABSTRACT iv
LIST OF FIGURES viii
LIST OF TABLES ix
1 Introduction 1
2 Theory and Computational Details 5
2.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 The Thomas-Fermi Model . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 The Hohenberg-Kohn Theorems . . . . . . . . . . . . . . . . . . 8
2.1.3 The Kohn-Sham Equations . . . . . . . . . . . . . . . . . . . . . 11
2.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Vienna Ab-initio Simulation Package (VASP) . . . . . . . . . 16
2.2.2 Band Topology Calculation . . . . . . . . . . . . . . . . . . . . . . 17
3 Results and Discussion 18
3.1 Structure Model for III-V Films . . . . . . . . . . . . . . . . . . . . 18
3.2 Lattice Parameters, Band Gaps, and Z2 Invariant . . . . . . . . . . 20
3.3 Structural Analysis of the Selected Six Films Under Strain . . . . . 23
3.4 Electronic Structures of III-V Films Under Strain . . . . . . . . . . 25
3.5 Effect of Hydrogenation to Band Structures and Density of States . 27
3.6 Robustness of TlBi Against Different Hydrogen Coverages . . . . . 30
3.7 Topological Edge States of TlBi Ribbons . . . . . . . . . . . . . . . 32
4 Conclusion 34
References 35
A Supplementary Materials 39

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