在本論文中我們運用緊束縛模型來研究奈米石墨帶,石墨氫化物,以
及奈米鍺帶的電子或光學特性。首先,我們研究非對稱雙層石墨帶,
發現其藍道能階的破壞並伴隨著電子在次晶格中轉移,同時也發現其
結果也與實驗觀測到的現象吻合,另外,在氫化的石墨中,由於共價鍵
結造成其有很大的能隙,我們自行尋找緊束參數並發現其能幾乎完全
擬合第一原理結果,同時我們也經由計算軌域投影態密度,並由此發
現並解釋其豐富的光學特性,特別的是我們發現由軌域混成所造成的
光吸收譜的藍位移現象,最後,我們研究有著微曲幾何結構的鍺奈米
帶,我們發現到由於自旋軌道耦合效應,量子侷限效應,外加場效應彼
此間的競合而造成許多較奈米石墨帶更為豐富的電子性質。

This dissertation studies the magneto-electro properties of graphane asymmetric bilayer hydrogen -adsorbed nanographene, and germanene nanoribbons with buckling structures. Magneto-electronic properties of asymmetric bilayer nanographene ribbons are enriched by variation in their geometric structures, interlayer atomic interactions, magnetic quantization and finite-size confinement. Large changes in band symmetry, degeneracy of the partial flat bands, number of band-edge states, energy dispersion, carrier density, and spatial symmetry of the wave function, may be experimentally generated by various manipulations. Quasi-Landau levels can be converted into oscillating bands with the creation of associated additional band-edge states. When the upper ribbon is located over the lower ribbon longitudinal mid-line, the Landau wave functions are completely destroyed, and a charge transfer between different layers or different sub-lattices in the same layer occurs. Furthermore, the density-of-states, reflecting the band structure, shows large changes in terms of the number, structure, energy, and height of the prominent peaks.

The tight-binding model is here developed to study the electronic and optical properties of graphane. Strong sp3 chemical bonds among the carbon and hydrogen atoms induce a special band structure and thus lead to a rich optical excitation pattern. The absorption spectrum is largely independent of the direction of electric polarization. It exhibits complex shoulder structures and absorption peaks, respectively arising from the extreme and saddle points of the parabolic bands. Threshold optical excitations, solely associated with the 2px and 2py orbitals of the carbon atoms, are revealed in a shoulder structure at ∼3.5 eV. The first symmetric absorption peak, appearing at ∼11 eV, corresponds to energy bands caused by the considerable hybridization of carbon 2pz orbitals and H 1s orbitals. Some further absorption peaks at higher frequencies indicate bonding of the 2s and 1s orbitals. These results are in sharp contrast to those for sp2 graphene systems.

Germanene nanoribbons with buckling structures are also found to exhibit unique electronic properties. We describe complex interactions among quantum confinement, spin-orbital coupling, magnetic quantization and electric field, which dominate quantum numbers, energy dispersions, energy gap, state degeneracy, and wave functions. Such mechanisms can diversify the spatial charge distribution and spin configurations on distinct sub-lattices. Specifically, there exist two pairs of unusual energy bands near the Fermi level. The rich electronic structures are reflected in a range of special density-of-states structures. The predicted results could be directly verified experimentally by scanning tunneling spectroscopy.

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