我們利用緊束模型來研究扭轉雙層石墨烯的基本電子性質。主要考量擁有擴大晶胞的可匹配雙層系統。同層之間僅有2pz軌域的π鍵結，但不同層之間存在複雜的π鍵結和σ鍵結。這些交互作用引起豐富的電子特色，包含以費米能為中心能帶上下不對稱、線性與拋物線能帶、等方與非等方性共存、價帶與導帶重疊形成半金屬和每一條能帶擁有幾個臨界點。能帶特色是由扭轉角度所決定，同時直接反應於態密度。DOS呈現許多肩膀以及對稱發散峰的二種結構，它們分別來自於極值點和馬鞍點。

We use the generalized tight-binding model to study fundamental electronic properties of twisted bilayer graphene. The main consideration is on a system which has mutual enlarged cell. The carbon atoms on the same layer only include the π bond in 2pz orbital. On the other hand, there exist the complex π and σ bonds between the different layers. These interactions lead to the extensive electronic properties. The energy band structure presents the asymmetric linear, parabolic energy bands with isotropic and non-isotropic coexistence. The valence and conduction bands overlap each other to form a semi-metal. The critical characteristics of the energy bands are determined by the twist angle which is directly reflected into the density of states (DOS). The DOS spectrum presents shoulder structure and symmetrical divergence peaks. They are, respectively, related to the extreme points and saddle points.

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