本篇論文中，在隨機相位近似下研究了單層石墨庫倫激發以及去除激發的問題。由於零能隙的特徵，單層石墨顯示了豐富的低頻激發譜。激發譜裡包含了能帶帶內、帶間的電子電洞激發以及電漿子。其中，後兩者純粹是溫度所引起的。費米動量態的去除激發機制只透過帶間的電子電洞激發。而對於其他狀態，三種激發過程的都對衰變率有所貢獻。在隨機相位近似下，我們推導出層狀石墨系統的庫倫激發公式。並且針對兩種典型的雙層石墨堆疊系統，研究了它們的庫倫激發特性。結果顯示，它們的特性與堆疊的序列、層間庫倫相互作用以及動量轉移有很大的關係，然而溫度與動量的方向則影響很小。另外，利用緊束模型，探討了單層石墨在外的空間調制電場和磁場下的電子結構。電子性質受到調制場的大小、方向和週期強烈地影響。它大大地改變了簡併度、能量色散、能帶間距、波函數和能帶邊界態。因此，相應的態密度出現了許多的特殊結構。

In this thesis, coulomb excitations and deexcitations of a monolayer graphite are
studied within random-phase approximation. A monolayer graphite exhibits rich low-frequency excitation spectra, mainly owing to the zero-gap characteristic. There exist interband e-h excitations, intraband e-h excitations, and plasmon. The latter two are purely caused by temperature. Interband e-h excitations are the only deexcitations mechanism for Fermi-momentum state. As to other states, three kinds of excitations are responsible for decay rates. The formulas of coulomb excitations for multilayered graphite are derived within random-phase approximation. Coulomb excitations of two typical bilayer graphites with different stacking sequences are studied. They are strongly affected by the stacking sequence, the interlayer coulomb interaction, and the momentum transfer. However, they hardly depend on the direction of momentum transfer and the temperature. The electronic structure of a monolayer graphite under the spatially modulated field is studied by tight-binding model. Electronic properties strongly depend on the strength, the direction, and the period of modulated fields. Such fields could lead
to the drastic changes in state degeneracy, energy dispersions, band spacings, wave functions, and band-edge states. Hence, density of states exhibits several special structures.

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