以時間相關密度泛函理論研究二維和三維六方碳和硼化氮材料之電漿子激發

Abstract

近代科學對於二維石墨烯的大量研究，起自於2004年Andre Geim 和Konstantin Novoselov 在曼徹斯特大學的實驗室中，成功用膠帶把二維石墨烯從石墨晶體中分離出來。由於石墨烯本身獨特的各種物理性質，全球的科學研究者都為之瘋迷，尤其是因為其線性的電導率，一般認為是在倒晶格中，費米面K對稱點上的狄拉克錐所造成。二維石墨烯是由是由蜂窩形狀碳元素所排列而成的二維晶體，碳原子上的電子主要是 軌域混成。透過對於電子能量散失能譜的研究，我們可以理解到，二維與三維石墨烯對於動量與能量的色散關係，以及對於電導性的影響。 類似的蜂巢型結構也可以在二維和三維的六方硼化氮中被發現。它們和六方石墨烯有類似的結構，但是在物理性質上卻有本質上的不同。其中石墨烯為導體，而硼化氮為半導體。在此我們也會討論二維六方硼化氮的電子能量散失能譜。 我利用時間相關密度泛函理論，來計算一系列不同的傳導動量所對應到的電子能量散失能譜。我也會對於倒空間中不同動量方向電子能量散失能譜，討論各向異性的現象。另一方面，我也會於二維和三維六方結構的材料中，討論不同特徵的電漿子激發。

The recent studies in graphene have been prosperous since the first isolated graphene from graphite with a tap in 2004 by Andre Geim and Konstantin Novoselov in a laboratory at the University of Manchester. The special physical properties of graphene have been attractive to researches around the world, including the linearized conductivity, believed to be caused by Dirac cone at the K point in the reciprocal lattice. Fundamentally, graphene is just a two-dimensional honeycomb lattice composed of carbons, with four valence electrons of sp¬¬2 hybridized density distribution. Through a study of electronic energy loss spectrum of graphene and graphite, one can observe the different patterns of dispersion relation of momentum and frequency and further, conductivity. A similar honeycomb structure may also be found in hexagonal boron nitride and the single boron nitride sheet. Hexagonal boron nitride is of a similar structure with graphite but with very different physical properties. Although graphite is a conductor, the graphitic boron nitride, also called hexagonal boron nitride, is a semi-conductor. The single boron nitride sheet is also an interesting structure for the electron energy-loss spectra study. In this thesis, I calculated the electron energy-loss spectra with a sequence of different transferred momenta which are relatively small against the ones of incident electrons by applying time-dependent density-functional theory. Here I will discuss the anisotropy of plasmon excitations for momentum transferred in different directions; further, the different patterns of plasmon excitations in two- and three- dimension hexagonal structural materials.