本論文以緊束模型探討一維 (1D) 奈米石墨帶的電子性質。這些不同石墨帶的電子性質，隨著石墨帶幾何構造、所外加的電場以及磁通量而有著特性上的變化。首先，對層狀石墨帶而言，層與層之間的交互作用顯著地影響能帶構造、能隙、自由載子以及態密度。這些態密度顯示著許多特殊的構造，包含平台構造、不連續構造以及發散譜線。其次，有效電場可以調制能帶構造、改變能帶間隔、產生許多新的邊界能態、調節能隙大小、並引發金屬 -- 半導體（或半導體 -- 金屬）之間的轉換。由有效電場造成的效應，將直接反應在態密度頻譜之中，諸如，特殊譜線結構的產生、譜線位置的移動、譜線強度的變化以及能隙大小的改變。此外，有效電場更深深地影響低能處的光吸收譜，期間有著：第一吸收峰頻率的改變；譜線強度的變化；甚至，有著新吸收峰的生成。石墨帶之低能量的光吸收譜同樣也受到磁場有效的調制，其中，磁場能改變1D拋物線能帶使之轉換成Hall-edge能級以及0D Landau能級。在磁場作用之下，高度簡併的Landau能級，能出現在足夠寬的石墨帶之能帶中，並且，石墨帶的寬度愈寬產生的Landau能級數也愈多。此外，石墨帶Landau峰的頻率及特殊譜線結構的數量，並不受石墨帶的寬度改變而有所影響，主要是隨著外加磁場而變化的。上述之結果，有助於我們對石墨之磁電子性質、磁電子激發及磁光吸收譜的計算。

Electronic properties of one-dimensional (1D) graphene nanoribbons were studied by the tight-binding model. They were strongly dependent on the geometric structures, the
electric field, and the magnetic flux. For the layered graphene ribbons, the interlayer interactions significantly affected band structure, energy gap, free carriers, and density of states (DOS). DOS exhibited many special structures, including plateau, discontinuities,
and divergent peaks. The effective electric field modified the energy dispersions, altered the subband spacing, produced the new edge state, changed the band gap, and caused the metal-semiconductor (or semiconductor-metal) transitions. Due to electric field, the effects
were completely reflected in the features of DOS such as the generation of special structures, the shift of peak position, the change of peak height, and the alternation of band gap. Moreover, the effective electric field had great influence on the low-energy absorption spectra. It could change frequency of the first peak, alter the peak height, and even produce the new peaks. The perpendicular magnetic field in graphene ribbons strongly modified
the low-energy spectra. It could change the 1D parabolic bands into the Hall-edge states and the 0D Landau levels. Landau levels appeared when the ribbon width was sufficiently wide. More Landau levels came out with the increase of width. The magnetic field dramatically
changed absorption peaks, such as the number, the intensity, the frequency, and the symmetric form. The absorption frequencies of the Landau peaks could hardly depend on the ribbon width while the opposite was true for the spectral intensity. The results mentioned above are useful in understanding a 2D monolayer graphite, e.g., magneto-electronic properties, magneto-electronic excitations, and magneto-optical absorption spectra.

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