以第一原理研究石墨、單層與雙層石墨烯在外加應力下的電學性質與光學性質

中文摘要由於石墨烯具有相當優秀的物理性質，因此一直是相當熱門的研究課題。本文以第一原理之密度泛函理論與含時密度泛函理論研究計算石墨、單層與雙層石墨烯在不同應變下的電學性質與光學性質，我們將考慮沿均向、扶手方向與鋸齒方向的應變。首先討論應變對其能帶結構與功函數的影響。最後，我們將研究材料在能量轉移波數向量( )沿著平面與垂直平面，且q值趨近於0的情況下之電子能量損失能譜(Electron Energy-Loss Spectroscopy，EELS)與應變的關係。我們會對不同近似方法作比較，其中包括絕熱局域密度近似(Adiabatic Local-Density Approximation，ALDA)與無規相近似(Random-Phase Approximation，RPA)，並討論局域場效應對EELS頻譜的影響。我們發現應變對石墨的電子結構效應與對AB堆疊之雙層石墨烯的效應相似，在費米能階附近與能帶相交所形成的眼睛形狀大小會隨著應變的增加而增加；應變對單層石墨烯的電子結構的效應則與對AA堆疊之雙層石墨烯的效應相似，在費米能階附近的與能帶相交形成的迪拉克點(Dirac point)會隨著應變的變化而移動。我們也研究上述系統在不同的應變下，功函數與應變的關係，發現功函數隨應變增加而增加並且在-16%至-40%間會有極值。我們也發現材料在能量轉移波數向量( )沿著平面時，有局域場效應與無局域場效應結果近似；垂直平面時，有局域場效應與無局域場效應結果則有較大的差異。能量轉移波數向量( )在沿著平面與垂直平面時，ALDA與RPA結果近似。因此在能量轉移波數向量( )垂直平面時，必須考慮局域場效應。關鍵字：含時密度泛函理論、石墨、石墨烯、雙層石墨烯、迪拉克錐、轉移波數向量、ALDA近似、RPA近似、局域場效應、EELS頻譜

關鍵字

ALDA近似；轉移波數向量；迪拉克錐；雙層石墨烯；石墨烯；石墨；含時密度泛函理論； RPA近似；局域場效應； EELS頻譜

並列摘要

Abstract Graphene has attracted increasing attention in both theory and application from researchers due to their outstanding mechanical and electronic properties. The purpose of this thesis was to use Density Functional Theory (DFT) and Time-Dependent Denisty Functional Theory (TDDFT) to determine both the electrical and optical properties of graphite, graphene and bilayer graphene under homogeneous, armchair and zigzag strains. The effects of the strain on both band structure and work function were evaluated. Moreover, the Electron Energy Loss Spectroscopy (EELS) of strained graphite, graphene and bilayer graphene were calculated with in-plane and out-of-plane of vanishing momentum transfer of the light. Furthermore, the different calculation methods, e.g., Random Phase Approximation (RPA) and Adiabatic Local-Density Approximation (ALDA), with and without inclusion of local-effects were calculated and compared. Results indicate that the strain effects on the electronic structure of graphite and AB stacking graphine were very similar. The size of eye shape, which was formed by the intersection of and bands near the Fermi level, increased as the applied strain increased. The strain effect on the electronic structure of graphene and bilayer graphene with AA stacking also shows very similar results. The Dirac point moved for stretching and compressed strain. We found that the work function of both monolayer and bilayer graphenes increased as the compressive strain increased and had a minimum at about -20%. Furthermore, for q parallel to the plane,the EELS of graphene and bilayer graphene inclusion of local-field effects show the similar results with those of exclude of the local-field effects. On the contrary, the local-field effects were found to be important for the EELS as q perpendicular to the plane. Key words: Time-Dependent Density-Functional Theory,Graphite, Graphene,Bilayer graphene,Dirac cone, Wave vector of light q,ALDA, RPA,Local field effect,EELS

並列關鍵字

Wave vector of light q ； Dirac cone ； Bilayer graphene ； Graphene ； Graphite ； Time-Dependent Density-Functional Theory ； ALDA ； RPA ； Local field effect ； EELS