在本文中碳相關奈米系統(奈米石墨帶，單層奈米碳管，以及BC3微管)的電子性質是由緊束模型計算。單層奈米碳管的介電常數ε是用 random-phase approximation計算。在長波極限下，L=1的ε表示對於均勻橫向電場的屏蔽能力。ε(q=0，L=1)幾乎不受旋角，微管半徑，磁通量與溫度的影響。在此，BC3微管的光學性質也被討論。因為很多一維能帶的存在，BC3微管展現豐富的吸收峰。對所有BC3微管而言，起始吸收頻率大概是0.15γ0。吸收譜對旋性，半徑，和磁通量的變化有很高的靈敏性。調製電場能有效的改變能量的色散，變更能量間距，產生額外的能帶邊界態，改變能隙大小以及引起半導體金屬轉換。在垂直磁場和調製電場下，能量色散和加在奈米石墨帶上的電位有密切的關係。在態密度中能帶結構的特徵將會直接的被反映出來。峰的數目，高度，位置，與形狀都強烈地被外加場所改變。這些場對光吸收譜有強大的影響。吸收峰的位置，高度，數目，以及起始激發能量都被改變。磁場的效應會和電場的效應彼此競爭。上述的結果將有助於我們對碳相關奈米系統的了解。

The electronic properties of carbon-related nanosystems (nanographene ribbons, singlewalled carbon nanotubes, and BC3 nanotubes) are calculated via the tight-binding model. The static dielectric function (ε) of single-walled carbon nanotubes is evaluated within the random-phase approximation. At long wavelength limit,ε of L=1 represents the screening ability for a uniform transverse electric field. The carbon nanotubes can strongly screen the uniform transverse electric field.ε(q = 0, L = 1) is less affected by the chiral angle, the nanotube radius, the magnetic flux, and the temperature. The optical properties of BC3 nanotubes are discussed. BC3 nanotubes exhibit rich absorption peaks in the overall frequency because of considerable one-dimensional energy bands. The threshold absorption frequency is ~0.15 γ0 for all BC3 nanotubes. Absorption peaks are sensitive to the changes in the chirality, the radius, and the magnetic flux. A modulated electric field could effectively modify energy dispersions, alter energy spacings, create extra band-edge states, change energy gap, and induce the semiconductor-metal transition. In the presence of the perpendicular magnetic field and the modulated electric field, the energy dispersions are closely related to the potential added to the ribbons. The density of states directly reflects the characteristics of band structure. The number, the height, the position, and the shape of peaks are greatly affected by the external fields. They have great influence on the optical absorption spectra. The position, the height, and the number of absorption peak and the threshold excitation energy are changed. The effects of the magnetic field would compete with those of the modulated electric field. The results mentioned above are useful in understanding the carbon-related nanosystems.

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