本篇論文以第一原理VASP的計算，研究一維雙層AA堆疊鋸齒狀奈米石墨帶的幾何結構與電子性質。自旋與自旋的交互作用包含Hamiltonian在裡面，同時考慮了4種不同自旋對稱結構。討論系統總能、能帶、能隙、態密度、簡併度、band-edge state、鍵長及層與層之間距離等物理量，並探討與各種自旋對稱結構和寬度的關係。AFM－AFM為能量最低且最穩定的系統。幾何結構只有在邊緣附近的才會有比較明顯的變化，而垂直方向自旋結構為AFM的彎曲量比FM大，電子的轉移也較多。以費米能為中心，4種自旋結構的導帶與價帶皆不對稱，而除了在費米能附近的部分平能帶，皆由拋物線能帶組成。層與層之間的交互作用引起許多高態密度的band-edge state，且皆會隨寬度變大而明顯改變。垂直方向自旋結構的不同，造成費米能附近能帶的簡併和分裂，這些能帶在布里淵區邊界的能量差（energy spacing）不會隨寬度變化而改變。平面自旋結構為FM皆存在金屬特性，而平面自旋結構為AFM則是有直接或間接能隙為0.05eV～0.5eV的半導體，此能隙皆會隨著寬度變大而變小。這些預測結果將可利用掃描穿隧式顯微鏡（STM）直接測量出來。

This work investigates the geometric structure and electronic properties of 1D bilayer graphene nanoribbons with AA-stacking and zigzag edge. The Hamiltonian contains the spin-spin interactions, and 4 spin-symmetric structures are simultaneously taken into consideration. We discuss the physical quantities such as the total energy of the system, energy band structures, bonding length as well as interlayer distance, and study the relationship between various spin-symmetric structures and widths. The AFM-AFM has the lowest energy and is the most stable system. The geometric structure shows obvious change only near the edge. The structure with the AFM in the vertical direction exhibits greater curvature and more electron transfer. With respect to the Fermi level, the conduction and valence bands are asymmetric among these four spin structures, and all bands are composed of parabolic ones except the flat bands near the Fermi energy. The interlayer interactions lead to a great deal of band-edge states contributing to the high DOS, which changes obviously along with the increase of the widths. Different spin structures in the vertical direction cause the degeneracy and the splitting of bands near the Fermi energy. The energy spacing at the first Brillouin zone’s boundaries does not vary with the widths. The FM structures result in the characteristics of metals, and the AFM ones belong to the semi-conductors with direct or indirect energy gap of 0.05eV～0.5eV. These gaps will decrease when the widths increase. The predictions could be verified directly by the scanning tunneling microscopy (STM).

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