摘要
本文利用緊束模型計算單層石墨烯能帶結構，並利用介電函數虛部和電子激發的關係，研究單層石墨烯在溫度(T)及摻雜條件下，低頻的電子激發行為。溫度可改變電子分佈機率，摻雜可提升費米能階。研究中發現，若固定轉換動量(q)，在溫度或摻雜的單一條件下，會增強單粒子激發的強度，但激發的頻率並不會改變。由於低能的線性交叉能帶，溫度或摻雜的增加，可快速增多激發的初態及末態，以致增強激發強度。而激發頻率則會受到q的增大而升高。相同條件下，系統中也存在電子的集體激發(電漿子)。T，費米能，或q的增加皆可提升電漿頻率，而前兩者(最後者)會增強(降低)激發強度。若費米能不為零，激發強度或頻率對T改變並不存在簡單的關係。給定q且T由0開始增加，單粒子激發的強度先降低再增強，而頻率仍保持不變。電漿子的強度則先大幅降低再緩慢增強，其頻率亦會先下降然後再升高。這特殊的現象主要是由於費米能離開能帶交叉點時，溫度會使得來自不同能量區域量子態的激發產生競爭的效應。

Abstract
This thesis calculates the energy band structure of graphene by the tight-binding model. The low-frequency electronic excitations of monolayer graphene at different temperatures and various doping conditions are studied using the imaginary part of the dielectric function. Temperatures change the distribution of electron probability density, while doping raises the Fermi level (EF). We find that when the transition momentum (q) is fixed, the single-particle excitations increase under the single condition of temperature or doping, but the excitation frequency is not affected. Due to the linear energy band intersecting at low energy, the increase of temperature or doping level rapidly enlarges the numbers of initial and final states of excitations so that the intensity is enhanced. On the other hand, the greater q leads to the higher excitation frequency. Under the same condition, there are collective electronic excitations, also known as plasmon. The rise in T, EF or q all increases the plasmon frequency ; both of T and EF intensify the excitation, while q lowers it. If EF≠0, the excitation intensity and frequency possess no simple relationship with temperature. At a fixed q, the intensity of single-particle excitation is firstly weakened and then enhanced when increasing the temperature from zero, while the frequency remains. As for the strength of plasmon, it declines greatly in the beginning and slowly ascends. Similar tendency applies to the frequency. This peculiar phenomenon takes place mainly due to the competition between quantum-state excitations from different energy regions caused by temperature when EF departs away from the linear intersection.

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