摩爾定律是近代矽碁半導體的發展準則:根據摩爾定律，單位面積所能容納的電晶體數量每18個月必須倍數成長，其對應的製程成本為前一個世代的一半。然而依照目前科技的進程，元件尺寸的微縮到一定的尺度後將碰觸到其物理的極限，形成短通道效應，並造成漏電流的增加。為了跳脫相關的束縛，人們提出了數種因應的方案，例如: 鰭式電晶體，系統單晶片化，半導體材料的替換(如:氮化鎵， 石墨烯以及過度金屬硫族化物…等)，以及自旋電子學和能谷電子學的發展。在其中，能谷電子學即是利用二維六角晶格材料中獨特的能谷自由度作為操作單元，能谷自由度雖然與自旋電子有著相似的機制，卻是由於不同的物理本質所產生。這本論文主要是著重在計算鋸齒狀二維六角晶格奈米帶中的能谷磁矩，來了解能谷自由度的物理特性，並進一步討論施加外來電場所造成的能谷磁矩電流及能谷霍爾導電率，來展現能谷電子學的現象。

這本論文由以下幾個章節構成，章節一介紹了基本的二維材料，並從物理的觀點來探討能谷自由度在二維六角晶格材料產生的原因。章節二首先討論了鋸齒狀二維六角晶格奈米帶理論模型的建立，並利用了不同的方法來計算能谷磁矩在不同的鋸齒狀二維六角晶格奈米帶的大小。章節三則是數值的結果及分析，以及對這本論文的總結。

Moore’s law has been the guideline of silicon-based FETs (field-effect transistor) in modern electronic industry. As described by Moore’s law, the number of FETs is doubled in a given area in every 18 months. However, the continuation of this trend eventually meets its challenges due to a downgrade of device performance with the miniaturization, e.g. current leakage and short-channel effect. To overcome these difficulties, several technological options have been proposed. For instance, the development of FinFETs, building systems on chip (SoC), substitution by potential semiconductor materials such as GaN, graphene, transition metal dichalcogenides (TMDCs), and new device concepts like spintronics and valleytronics. For valleytronics, it exploits the manipulation of unique valley degree of freedom in 2D hexagonal materials in a way analogous to that with spin in spintronics but with significant differences in the physical concepts. In this thesis, we explore the valley pseudospin physics of zigzag nanoribbons in 2D hexagonal materials, in particular, the magnetic moment in association with the valley pseudospin. Moreover, we study the valley magnetic moment current and valley Hall conductivity of the ribbons under external electric field to illustrate valley physics in these structures.

This thesis is separated into several parts. Chapter 1 is the introduction of 2D hexagonal materials, and reviews the fundamentals of valley physics in 2D materials from physical viewpoints. In Chapter 2, we build the discrete tight-binding models of graphene and TMDCs respectively. Various methods for calculating valley magnetic moments are also discussed in Chapter 2. In Chapter 3, we present numerical results with a discussion and also conclusion of this thesis.

Abstract--------------------------------------------------------- I

Acknowledgements------------------III

Contents--------------------------------------- IV

Chapter 1 Introduction to 2D materials-------------------------- 1

1-1 Monolayer Graphene (MLG)------------------------------------ 1
1-2 Transition Metal Dichalcogenides (TMDCs)------------------ 4
1-3 Fundamentals of valley physics in 2D materials----------------------------------- 6
1-4 The thesis------------------------------------------------------------------------------ 10

Chapter 2 Theoretical model of zigzag nanoribbons in 2D hexagonal materials

2-1 Theoretical model -------------------------------------------------------------------- 11
2-1-1 Zigzag graphene nanoribbons ---------------------------------------------- 11
2-1-2 Zigzag TMDCs nanoribbons ----------------------------------------------- 14
2-2 Theoretical formulation for the study of graphene nanoribbons--------------- 17
2-3 Theoretical formulation for the study of TMDC nanoribbons --------------- 21



Chapter 3 Results and discussion----------------------- 24

3-1 Results for zigzag graphene nanoribbons-------------------- 24
3-2 Results for zigzag WSe2 nanoribbons------------------------ 29
3-3 Discussion and conclusion--------------------------------- 33
References----------------------------------------------------- 34

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