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研究生:李偲豪
研究生(外文):Lee, Shih-Hao
論文名稱:形變對少層石墨之電子結構和光學激發的影響
論文名稱(外文):Deformation effects on electronic structures and optical excitations of few-layer graphenes
指導教授:林明發林明發引用關係
指導教授(外文):Lin, Ming-Fa
口試委員:盧炎田溫清榕張振鵬蔡炎熾吳璧如
口試委員(外文):Yan-Ten LuChing-Rong WinCheng-Peng ChangYan-Chr TsaiPi-Ju Wu
口試日期:2010-07-16
學位類別:博士
校院名稱:國立成功大學
系所名稱:物理學系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:106
中文關鍵詞:少層石墨AA堆疊AB堆疊單軸應力形變能帶光譜等方性
外文關鍵詞:few-layer graphenesAA stackedAB stackeduniaxial stressdeformationenergy bandspectraisotropy
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我們透過緊束模型來研究單層、AA 堆疊和AB 堆疊多層石墨在形變下的電子特性。而經由梯度近似計算出的光子激發則直接反應了能帶邊界的主要特性。石墨層上應變力的力學機制則是以彈性理論為基礎。單軸應力大大的改變了能帶的色散關係、能帶邊界、費米動量、能帶簡併度,這些特徵都會反應在態密度和光譜。層跟層的原子交互作用力導致光譜出現顯著峰、肩狀結構和能隙。石墨層跟層之間的不同堆疊方式則會導致AA 堆疊石墨的低能能帶線性分布和AB 堆疊石墨的低能能帶拋物線分布,這些不同的能帶分布將會造成極端不同的光譜結構。而這些光譜結構同時也會受到石墨層數的影響。在沒有形變下,AA、AB 堆疊少層石墨的第一布里淵區顯現六角對稱性,然而能帶呈現極度的非等方性。由於速度矩陣元素和聯合態密度之間關係的影響,能帶的非等方性並沒反應在光譜上。雖然所有頻率下的速度矩陣元素平方積分也是呈現非等方性。在單軸應力的作用下,形變破壞了第一布里淵區的六角對稱性,也改變了能帶色散和速度矩陣元素之間的關係。因此光譜的等方性被應變力給破壞了。以上所預測的結果將有助於驗證二維少層石墨的實驗量測。
The electronic properties of monolayer- , AA-stacked and AB-stacked multilayer graphenes under deformation are studied by the tight-binding model. The optical excitation spectra, directly reflecting the main characteristics of band-edge states, are evaluated within the gradient approximation. The mechanical effects of strain on graphene are based on the elasticity theory. The uniaxial stress drastically changes the energy dispersion, band-edge states, Fermi momenta, state degeneracies, which reflects on the density of states and absorption spectra A(w). The interlayer atomic interactions induce prominent peaks, shoulder structures, and transition gaps in optical excitations. The stacking sequences respectively lead to linear and parabolic low-energy bands for AA- and AB-stacked graphenes, resulting in extremely different optical structures. These optical features are also influenced by the layer number. In the absence of uniaxial stress, the first Brillouin zones (1st BZ) of both AA- and AB-stacked few-layer graphenes exhibit a hexagonal symmetry; nevertheless, their band structures show strong anisotropy. Such anisotropic properties are not revealed in absorption spectra, owing to the relations between the velocity matrix elements and the joint density of states, even though the integrals of square of velocity matrix elements possess anisotropy for all frequency. Under the uniaxial stress, deformation breaks the hexagonal symmetry of the 1st BZ, and changes the relations between the energy dispersions and the velocity matrix elements. Thus isotropic spectra are also destroyed by strain. The predicted results would be useful in identifying the experimental measurements on two-dimensional few-layer graphenes.
1 Introduction 1
1.1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Uniaxial-stress effects on electronic structures of monolayer and bilayer
graphenes 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 The tight-binding model with deformations . . . . . . . . . . . . . . . . . . 13
2.3 Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Optical properties of deformed few-layer graphenes with AB stacking 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 The tight-binding model with deformation . . . . . . . . . . . . . . . . . . 42
3.3 Low-energy electronic and optical properties . . . . . . . . . . . . . . . . . 48
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Isotropy of optical excitations in few-layer graphenes 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Electronic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Absorption functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5 Deformation-Induced Anisotropy of Absorption Spectra in Bilayer Graphenes 76
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Electronic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2.1 Deformation of geometric structures . . . . . . . . . . . . . . . . . . 79
5.2.2 Tight-binding Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 Energy dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Deformation Effects on Absorption Spectra . . . . . . . . . . . . . . . . . . 86
5.3.1 Optical absorption functions . . . . . . . . . . . . . . . . . . . . . . 86
5.3.2 Joint density of states . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.3 Velocity matrix elements . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.4 Optical absorption spectra . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Summary 103
chapter 1
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chapter 3
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chapter 4
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