在這篇論文之中，我們以緊束模型研究少層石墨(~1-4層)的電子結構，這些不同石墨系統的電子性質將隨著層數、堆疊方式、沿armchair以及zigzag方向應力強度而有著特性上的變化。首先，「層和層間交互作用效應」會劇烈地改變能帶色散關係、能帶寬度，並且產生新的邊緣能態。電子性質會反應在態密度，線性能帶在態密度上是有限值，邊緣能態反應在態密度上則是對數發散或開根號發散的峰。石墨晶格在外加應力下的「形變效應」適用於彈性理論，沿x軸應變量，在y軸和z軸相應不同應變量。根據Harrison’s rule，在形變下，同層以及層和層間的交互作用隨碳-碳原子間的距離而調整。
單層石墨於形變下線性能帶交點位移，但仍是半導體特質，形變改變雙層AB的能帶特性，造成半金屬-半導體轉換，三、四層的少層石墨因層數增加，堆疊結果越趨複雜。另外，少層石墨系統沿armchair方向拉長（壓縮），幾何結構類似沿zigzag方向壓縮（拉長）。「形變效應」改變同層與層間碳原子的交互作用，引起大量的費米動量位移，強烈改變低能的能帶分佈，變化自由載子的濃度，形變也導致態密度圖上出現明顯的峰。這些預測出的電子性質可由掃瞄穿遂譜驗證。

In this thesis, the electronic structures of few-layer graphenes (~1-4 layers) are investigated by the tight-binding model. They are significantly affected by the number of layers, the stacking sequences, and the intensity of stress along armchair and zigzag directions. The effects of interlayer interactions would cause the drastic changes in the energy dispersions, the band widths, and the new band-edge states. The electronic properties could reflect in the density of states (DOS) per unit area. The linear subbands correspond to finite values in DOS. The band-edge states exhibit the peaks of logarithmic divergences or square-root divergences. The deformation effects of graphene lattices under external stress are applied to the elasticity theory. The strain along x-axis is relevant to different values along y-axis and z-axis. Both intralayer and interlayer hopping integrals would be adjusted by the deformed C-C bond lengths, according to the Harrison’s rule.
The linear bands intersection of graphene shifts under deformation, but it still remains zero-gap semiconductors. The deformation influences energy bands and causes the semimetal-semiconductor transition in AB-stacked bilayer graphene. The stacking consequence would be more complicated in tri- and quadri- layers due to the increasing number of layers. In addition, the geometric structures of the tension (compression) along armchair direction are similar to those of the compression(tension) along zigzag direction for few-layer graphenes. The deformation effects would alter intralayer and interlayer hopping integrals between C-C atoms, the large shift of the Fermi momenta, the strong modification of low band structures, and the change of free carrier concentrations. It also leads to the prominent peaks in DOS. The predicted electronic properties could be verified by the scanning tunneling spectroscopy.

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