本篇論文以緊密束縛模型與梯度近似來探討成對單壁奈米碳管的電子能帶結構與光學性質。在碳管與碳管之間的電子穿隧作用影響，電子能帶與光學性質皆與碳管間的堆疊方式有密切關係。在費米能附近的管間交互作用主要可分為兩種：(1) 對應到單層石墨相同倒晶格點的管間交互作用與 (2) 對應到相反倒晶格點的交互作用。前者主導手椅狀與異螺旋碳管對的低能性質，而同螺旋碳管對則由後者主導；對鋸齒狀碳管對而言則是兩種交互作用皆存在。我們得計算結果預測了由少數根相同碳管堆疊的系統具有與單一碳管或大型碳管束即為不同的電子性質。此外，成對碳管的能帶結構可透過施加不同方向和強度的電場或磁場來調製，而我們發現一個沿著特定方向的微擾電場或磁場可以抑制碳管間的交互作用。當碳管對中的電子受到光子激發時，只有相同對稱性的佔據態與非佔據態間才允許躍遷，因此具有不同對稱性的次能帶的能量排列順序完全決定的光學吸收譜上的特徵。而結合外加場抑制管間交互作用的特性，我們的計算結果可用於判斷光學吸收譜上的特徵是否源自管間交互作用，進而了解碳管系統中的堆疊方式與少根碳管束中的獨特性質。

The tight-binding model with the gradient approximation is employed to study the band structures and the optical absorption spectra of pairs of single-wall carbon nanotubes. With intertube interactions, both electronic and optical properties are sensitive to the stacking types. The low-energy intertube interactions can be identified as electron hopping between (i) K and K, as well as (ii) K and K' points on each tube. The former dominates the energy dispersion near Fermi level for armchair and heterochiral pairs while the later for homochiral ones. Both types of interactions take place for zigzag pairs. As a result of the stacking-type dependence of intertube interactions, the low energy dispersions of identical two-tube or few-tube bundles are predicted to differ from single tubes or large bundles. Modulation of the band structures can be achieved by applying magnetic or transverse electric fields, depending on the field strength and field direction. Furthermore, a weak field along particular direction could suppress the effects of intertube interactions. For optical excitations, the symmetry or antisymmetry of wave functions determines the selection rules. The number, the height, and the position of absorption peaks are dominated by the subband energy sequence. Besides, the subpeaks due to intertube interactions could be discriminated from those of single tubes through applying a weak transverse electric field.

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