在本論文中利用了緊束模型來研究單層石墨在外加空間調制電場下的電子性質，如能帶結構及態密度。外加調制電場分別沿著armchair及zigzag方向：當外加調制電場於armchair方向時，在Fermi energy附近的能帶簡併會被破壞，且於Fermi energy上而產生新的states。能帶結構上則出現許多saddle points。1(gamma-0)附近的能帶簡併亦遭到破壞，態密度上原本在1(gamma-0)處的對數發散峰則形成一帶有震盪結構的”高原”分布。在3(gamma-0)附近的能帶因外加電場而破壞簡併並分布於3+/-V0 (gamma-0)。態密度從原本在3(gamma-0)處的shoulder結構變成由3-V0開始下降，在3+V0處降至零；當外加電場於zigzag方向時，能帶及態密度的變化均類似armchair的情況，大致呈現isotropic的性質。

The tight-binding model is utilized to study the electronic properties of graphene under the influence of modulated electric fields. Most sub-bands that are affected by the modulated electric fields appear to be plat or dispersionless along the direction in which the electric fields are exerted except for some near the Fermi energy. The DOS at the Fermi level is proportional to V0, but not related to the wavelength of the electric fields when RE > 250. New band-edge states are generated in the following regions: ( 0 ~ V0 ) , ( 1 – V0 ~ 1 + V0 ) and ( 3 – V0 ~ 3 + V0). The corresponding peaks in DOS become more obvious with the increase of V0, but less evident when the wavelength is enlarged. The DOS seems to be isotropic with respect to the direction of the modulated electric fields.

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