本文中，我們發展一個廣義化的緊束模型來研究研究石墨烯相關系統的磁量子化現象，範圍包括一維彎曲石墨帶、奈米碳管以及二維不同堆疊的多層石墨烯。這些所有的系統都是由石墨烯平面建構而成。它們的基本物理性質依據不同的曲率、邊界及堆疊組態而呈現豐富的多樣性。多層石墨烯中，垂直方向的堆疊組態決定其獨特的藍道能譜。甚至某些特殊堆疊組態下藍道能階會彼此反交錯。在彎曲石磨帶以及奈米碳管中，其主要的物理性質來自於幾何結構和磁場間的競合關係。量子侷限效應會抑制藍道能階的生成，進而造成在不同曲率、邊界及磁場下的特殊光學選擇規則。我們比較理論計算與實驗，結果呈現一致吻合。我們也得到了一些未被實驗證實的新穎特色。這個工作視為對石墨烯相關系統的重要特性的基礎研究。

In this thesis, we develop a generalized tight-binding model to study the magnetic quantization in graphene-related systems, ranging from one-dimension curved graphene nanoribbons and carbon nanotubes to two-dimension multilayer graphenes with different stacking configurations. All of the systems are built from graphene sheets and the essential properties are diversified by the curvature, edge and stacking without the modifications on the graphene honeycomb structures. In multilayer graphene systems the stacking configuration along the perpendicular direction determines the unique Landau level spectra and leads Landau levels to anti-cross only in certain configurations. In curved graphene nanoribbons and carbon nanotubes, the main electronic properties result from the cooperative or competitive relationships between the geometric structure and a magnetic field. The depressed LLs due to the quantum confinement lead to the peculiar optical selection rules which change with the curvature, boundary and magnetic field. We have paid attention to compare the calculations with the experiments and have obtained some novel features not yet verified experimentally. This study is served as a fundamental base to the further researches on the important properties of the graphene-related systems.

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