在這篇論文中，我們研究的系統有一維的奈米石墨帶的兩種幾何形狀，鋸齒狀(zigzag)及手椅狀(armchair)(而手椅狀又可分為 的金屬及 的半導體電性)，主要是探討一維的奈米石墨帶，在呈現不同的彎曲角度外加電場之下的電子性質。而外加電場的的方向在這是採取平行於原本石墨帶的寬度方向(y方向)及正上方的垂直方向(z方向)。
在這我們所用的理論是單一π鍵結緊束模型，在只考慮最鄰近原子交互作用下去計算能帶結構。而根據所計算的能帶結構結果，我們去探討當一維的彎曲奈米石墨帶在外加的y方向及z方向電場作用下，跟同角度彎曲但不加電場的能帶做比較。再探討其能帶上金屬及半導體的變化及轉換，以及原本在費米能的平坦帶上所造成的簡併度及能隙的影響。此外也探討對應在態密度及波函數上的變化。
我們可發現當同一角度的一維的奈米石墨帶，在一均勻電場作用下，不管y方向或z方向，電場越大對能帶所造成的變化也會越大越劇烈。但當電場大小與方向固定，不同的彎曲角度時，在鋸齒狀與手椅狀的能帯、態密度及波函數上，會有不一樣及相對應的影響。最後，我們也討論當一維的奈米石墨帶彎曲成360度成一管狀結構時的電子性質。

In this thesis, we study the systems consisting of one-dimensional nanographene ribbons of two geometric edge configurations, zigzag and armchair, among which the latter owns either metallic electronic properties when N=3I+2 or, otherwise, semiconducting ones. We mainly focus on the electronic properties of nanographene ribbons bent at different angles under the influence of electric fields. The applied electric fields are parallel to the width of the original ribbon (y-direction) or perpendicular to it (z-direction).
The energy band structure is calculated by the single pi-bond tight-binding model with only the interaction between the most neighboring atoms taken into account. The effects of electric fields along y- and z-directions on curved nanographene ribbons are detailedly investigated according to the calculated results. We further discuss the changes and transitions in the energy bands from the perspective of metal and semiconductor. In addition, the degeneracy and the gap in the flat bands at the original Fermi level, as well as the corresponding modifications on the DOS and wave functions, are also studied.
It is fount that, at a fixed bending angle, the greater the field strength is, the more severe influence it will induce for both y- and z-directions. On the other hand, various bending angles cause different effects on the energy bands, the DOS, and the wave functions of armchair and zigzag ribbons. Finally, we discuss the electronic properties of a tubular structure formed by bending one-dimensional nanographene ribbon at THETA = 2PI.

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