由於現今電腦的發展，以第一原理方法研究物理是非常普遍的。二維材料已
經成為當今熱門的研究主題。二維的磁性材料更是當今潮流。大多數的二維磁性
材料是絕緣體或金屬。由第一原理計算，我們預測一個新的二維半金屬材料。這
十幾年來，黑磷是一個很重要的二維材料。而它的各種缺陷已經被很多人所研究
唯獨缺少鉑。由於鉑與黑磷具有很高的合成能、黑磷經常是正摻雜，以及鉑具有
高的功函數。因此我們分析了由鉑嵌入黑磷的可能。
具有比較弱的層與層之間作用力的二維材料使得製造異質結構容易。由不同
材料所組成的異質結構可以有很廣泛的應用與新穎的物理性質。例如鄰近效應的
可能。於物理上，我們試著說明由 TaS2的電荷密度波誘導至石墨烯上的現象。於
應用層面，我們用 WSe2與 Fe3GeTe2製造一個可以控制自旋注入的裝置。
本文的安排如下：在第一章我們先介紹一些相關的研究與動機。基本的方法
在第二章節描述。在第三章我們預測了一個新穎的二維材料。於第四章我們討論
了黑磷的缺陷。第五章討論了電荷密度波的鄰近效應。最後，第六章敘述使用二
維磁性材料 Fe3GeTe2電子元件之特性

The ab-initio method to study physics is popular nowadays due to the development of computer. Research on two-dimensional (2D) materials has become a prominent topic. The 2D magnetic materials become a sensation nowadays. Most of 2D magnetic materials are insulators or metals. We predicted the new 2D half-metal material by density functional theory (DFT). Black phosphorus (BP) is an important 2D material in a decade. Different types of defects in BP are studied well except for Pt. Pt has high formation energy on BP. BP appears to be p-doped and Pt has high work function. Thus, we analyzed the defect of BP caused by Pt intercalation.
2D materials which have weak interaction between layers makes it feasible to create heterostructures. The heterostructures made of different materials have a variety of applications and novel physical properties such as proximity effect. On one hand, we show that there is a CDW proximity effect induced by TaS2. On the other hand, we used WSe2 and Fe3GeTe2 to make a device to control spin injection.
This thesis is organized as following: We give the introductions and motivations in chapter 1. We introduce the basic methods in chapter 2. Chapter 3 displays our prediction for new magnetic two-dimensional materials. We discussed the defect of black phosphorene in Chapter 4. In Chapter 5 we discussed the proximity effect of charge density wave. Finally, Chapter 6 provides an electronic device using two-dimensional magnetic material Fe3GeTe2.

Abstract
Chapter 1. Introduction 1
1.1 Two-dimensional Magnetic Materials 1
1.2 Defects of Black Phosphorus 3
1.3 Charge Density Wave of TaS2 and Proximity Effect 6
1.4 Valley Polarization 8
Chapter 2. Theoretical Background 10
2.1 Density Functional Theory 10
2.2 Wannier Function 18
2.3 Twilight and Dawn of two-dimensional magnetic material 24
2.4 Estimate Curie Temperature 26
Chapter 3. New two-dimensional magnetic materials EuOX 30
3.1 Computational Details 30
3.2 Results and discussion 31
Chapter 4. Defects in Black phosphorus 43
4.1Computational Details 43
4.2 Results and discussions 44
Chapter 5. Gyotaku of charge density wave from TaS2 to Graphene 55
5.1 Computational Details 55
5.2 Results and discussions 56
Chapter 6. A theoretic explanation of Electric control of valley polarization 74
6.1 Computational Details 74
6.2 Results & discussions 75
Bibliography 84
Appendix 101

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