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研究生：	鍾獻慶 Chung, Hsien-Ching
論文名稱：	單層與雙層奈米石墨帶的電子及光學性質 Electronic and Optical Properties of Monolayer and Bilayer Graphene Nanoribbons
指導教授：	林明發 Lin, Ming-Fa
學位類別：	博士 Doctor
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2011
畢業學年度：	99
語文別：	英文
論文頁數：	146
中文關鍵詞：	奈米石墨帶、電子性質、光學性質
外文關鍵詞：	graphene nanoribbon, electronic property, optical property
相關次數：	點閱：450 下載：24
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石墨烯是最近在凝態物理中一個很熱門的研究領域。這個系統有很獨特的物理性質，像是在費米能附近的線性能帶、具有極高的載子遷移率、半整數的量子霍爾效應等，這些現象均已被報告並刺激出很多其他的研究。奈米石墨帶可以從切割石墨烯獲得，其中有兩種典型的切割方向：鋸齒狀及手椅狀切割方向。在本文中，使用緊束模型來研究單層與雙層奈米石墨帶的電子及光學性質。許多物理性質，包含能帶、態密度、光學吸收譜等皆與邊界形狀有關，這些在內文中都有詳細的討論。另外，在光學吸收譜中的選擇律可以從波函數的角度去分析，這部份的內容則獨立為一個章節。並且，層跟層之間的交互作用及奈米石墨帶於外場下的性質則放在最後。

Graphene is recently one of the most active research areas in condense matter physics. The unique physical properties, such as cone-like energy spectra, extremely high mobility carriers, fractional quantum Hall effects, and Klein tunnelling have been reported and stimulated enormous amount of studies. Graphene nanoribbons (GNRs) are available from cutting the graphene sheet along a specific direction. There are two typical types of GNRs, i.e., zigzag and armchair GNRs. In this dissertation, the electronic and optical properties of monolayer and bilayer GNRs are investigated through the tight-binding method. The physical properties including energy spectra, density of states, optical absorption spectra, which exhibit many edge-dependent features are discussed in detail. Interestingly, the optical selection rules can be explored from the wave functions, which is presented in a single chapter. Furthermore, the effects of interlayer interactions and external fields in bilayer GNR system are
discussed in the last.

List of Figures viii
List of Tables xi
Abstract xii
Abstract in Taiwanese xiii
Acknowledgements xiv
Introduction 1
1 Graphene, a new class of materials . . . . . . . . . . . . . . . . . . . . . . . 1
2 Allotropes of carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Some properties of graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 The discovery and synthesis of graphene . . . . . . . . . . . . . . . . . . . . 9
5 From graphene to graphene nanoribbon . . . . . . . . . . . . . . . . . . . . . 12
6 Synthesis of graphene nanoribbon . . . . . . . . . . . . . . . . . . . . . . . . 13
7 the organization of this dissertation . . . . . . . . . . . . . . . . . . . . . . . 14
Theoretical Tool 15
1 Tight-binding method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Energy spectrum of trans-polyacetylene . . . . . . . . . . . . . . . . . . . . . 17
3 Energy gap in trans-polyacetylene . . . . . . . . . . . . . . . . . . . . . . . . 22
Graphene 24
1 Geometric structure and Brillouin zone . . . . . . . . . . . . . . . . . . . . . 24
2 Atomic orbitals of a carbon atom . . . . . . . . . . . . . . . . . . . . . . . . 26
3 sp2 hybridization in carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 σ- and π-bonds in graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Band structure considering only the π bonding . . . . . . . . . . . . . . . . . 30
6 Band structure considering both the π and σ bondings . . . . . . . . . . . . 31
7 Density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
8 Optical absorption properties . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Monolayer Graphene Nanoribbon 37
1 Geometric structures and Brillouin zones . . . . . . . . . . . . . . . . . . . . 37
2 Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.1 Band structures and DOS . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Magnetoelectronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Band structures and DOS . . . . . . . . . . . . . . . . . . . . . . . . 45
4 Optical absorption properties . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 Absorption spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Selection rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 Absorption spectra at finite temperature . . . . . . . . . . . . . . . . 56
Bilayer Graphene Nanoribbon 59
1 Geometric structures and Brillouin zones . . . . . . . . . . . . . . . . . . . . 59
2 Slonczewski-Weiss-McClure model (SWMcC model) . . . . . . . . . . . . . . 62
Effects of Transverse Electric Fields on Quasi-Landau Levels in Zigzag
Graphene Nanoribbons 63
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2 Tight-binding model with magnetic and electric fields . . . . . . . . . . . . . 64
3 Magnetoelectronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Edge-dependent Optical Selection Rules of Graphene Nanoribbons 75
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2 Tight-binding model and electronic properties . . . . . . . . . . . . . . . . . 76
3 Features of wavefunctions in real space . . . . . . . . . . . . . . . . . . . . . 78
4 Absorption spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5 Optical selection rules of GNRs . . . . . . . . . . . . . . . . . . . . . . . . . 83
6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Quasi-Landau Levels in Bilayer Zigzag Graphene Nanoribbons 88
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3 Magnetoelectronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Effects of Transverse Electric Fields on the Landau Subbands in Bilayer
Zigzag Graphene Nanoribbons 96
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Perpendicular Electric Fields on Quasi-Landau Levels of Bilayer Zigzag
Graphene Nanoribbons 112
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Conclusions and Outlooks 122
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
2 Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A A Hint for σ Bonding Calculation 124
B Chemical Potential μ(T) 125
C An Impressive Way to Demonstrate the AB-stacked GNRs 127
D Derivation of the Relations between Am±1 and Am in AGNRs 130
E Mirror Symmetry in GNRs 133
Bibliography 135
Permission Documents 141
Curriculum Vitae 144
List of Publications 145
                                    

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