旋轉石墨烯的電子性質研究

近年來研究旋轉雙層石墨烯的科學家日益增加,因為在過去的研究中,不論實驗及理論皆指出低能量自由電子會侷限在旋轉雙層石墨烯中的特定區域,這是在單層石墨烯中無法輕易實現的,因此旋轉多層石墨烯的電子性質是值得被研究的。在本論文中,我們利用緊束縛模型計算旋轉雙層石墨烯的能帶結構及局部態密度，首先會討論凡霍夫奇異點的起因及位置，基本上可以藉由我們導出來的數學式子中，得到合理的解釋。在小旋轉角度中,我們可以藉由局部態密度得知電子會傾向待在AA區域，而且我們可以從對角化矩陣後的特徵向量得知這些電子在此系統的分佈,依序我們可得知第一個侷限能態，電子將會有圓形的對稱性，而第二個會有$C_3$對稱性。接下來我們施予均勻的應變，結果顯示凡霍夫奇異點會由原本的兩個長至四個，我們提出一個忽略層與層之間作用力的緊束縛模型可以適當的解釋其結果。最後我們將系統考慮至旋轉三層石墨烯上，多個凡霍夫奇異點將會出現因為多層的作用力，此外我們還觀察到可以藉由凡霍夫奇異點的頂峰值，得知此凡霍夫奇異點是由哪兩層的作用產生。因此，希望我們的研究能對於旋轉多層石墨烯中的凡霍夫奇異點及電子被侷限在特定區域等相關問題有所幫助。

關鍵字

旋轉石墨烯；雙層石墨烯；緊束縛模型；凡霍夫奇異點；應變

並列摘要

Graphene consists of the carbon atoms in the honeycomb structure. There are many exceptional properties of the graphene has been found. One of the unique properties is called Klein paradox, which states that the massless Dirac electrons could not be confined in the one-dimensional region by the electrostatic potential. Interestingly, recently experimental and theoretical studies have shown that the low-energy Dirac electron would be confined in the graphene bilayer with a small twist angle. Therefore, it is worth while to study the problem. In our thesis, we will focus on the electronic properties of twisted graphene multilayers. At first, we would discuss the energy splitting of the Van Hove singularities and the real space distribution of the localized states in twisted bilayer graphene based on the tight-binding model. A clear mathematical formula is able to explain the occurrence of the Van Hove singularities. Our results also show that the real space distribution of the first and the second localized states would follow circular and $C_3$ symmetry respectively. Second, we construct an approximate model to explain why there are existing multiple Van Hove singularities in twisted bilayer graphene with external uniform strains. At last, our bilayer system extends to the trilayer system, and multiple singularities appear due to the multilayer interaction, and we proposed several ways to predict the energy splitting of these singularity groups. Besides, it is possible to realize the origin of each singularity from the peak values of the local density of states. Therefore, in the thesis, we study several electronic properties of twisted graphene multilayers and give meaningful explanations for each problem. Hopefully, our research is helpful to solve the Morie pattern puzzles in the twisted graphene multilayers.

並列關鍵字

twisted graphene multilayers ； twisted bilayer graphene ； tight-binding model ； Van Hove singularity ； strain

參考文獻

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旋轉石墨烯的電子性質研究

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