我們利用緊束模型來研究雙層碳相關系統的電子性質，包含有雙層碳微管、AB堆疊的雙層石墨以及微管-石墨層複合系統。可直接反應主要能帶特徵的光學及電子激發譜，則分別在梯度近似及RPA近似下來計算。層與層間交互作用顯著地改變低能電子態，將線性能帶轉換成拋物線能帶，也因此豐富了本身的激發性質。內外層微管間的相對平移和旋轉以及微管於石墨層上的堆疊情況，皆明顯地影響能隙、費米動量能態、能帶的色散關係及簡併度。於雙層手椅狀碳微管中，新邊界態間的光學躍遷會產生受溫度調制的吸收峰。此外，變動後的能帶提供了更多單電子庫侖激發途徑。電漿子的數目、強度、頻率及存在與否將強烈受到幾何結構及轉換角動量的影響。微管-石墨層複合系統的低頻能帶則是取決於微管的幾合結構及排列週期。至於在均勻磁場下的雙層石墨平面，層與層間交互作用相當程度地改變藍道能階的頻率及波函數，且進一步引發第二群藍道能態。這兩群藍道能階之間的電子躍遷會造成四組光學吸收峰。這些理論預測將有效來驗證層狀碳相關材料的實驗量測結果。

The electronic properties of bilayer carbon systems (double-walled nanotubes, nanotube-graphene composite systems, and AB-stacked bilayer graphene) are studied within the tight-binding model. The optical and electronic excitation spectra, directly reflecting the main characteristics of subbands, are evaluated within the gradient approximation and random-phase approximation, respectively. The intertube atomic hoppings significantly alter low energy states, change linear bands into parabolic ones, and thus enrich the intrinsic excitation properties. Energy dispersion relations, energy gap, subband degenercy, and Fermi-momentum states are strongly modulated in accordance with the translation and rotation between inner and outer nanotubes as well as the alignment of nanotubes on graphene sheet. In double-walled armchair carbon nanotubes, the optical transitions between new band-edge states result in temperature-dependent absorption peaks. Besides, the modified low energy bands provide more single-particle excitation channels during the Coulomb interactions. The number, existence, strength, and frequency of plasmon modes closely depend on the geometric configurations and the transferred momentum. Band structures of the nanotube-graphene hybrid systems are examined as well in terms of different nanotube sizes and alignment periods. As for bilayer AB-stacked graphene subjected to a uniform magnetic field, interlayer interactions substantially vary the energy and wave function of Landau states, and most importantly, bring about the second group of Landau levels. The optical excitations between the two groups of Landau levels with valence and conduction states lead to four kinds of absorption peaks. The predicted results would be useful in identifying the experimental measurements on stacked carbon materials.

Abstract....................... 3
Chapter 1. Introduction...................... 4
References..........................15
Chapter 2. Effects of geometric structures and temperature on electronic properties of double-walled armchair carbon nanotubes
2.1 Introduction.....................24
2.2 Theoretical calculation........25
2.3 Electronic and optical properties
2.3.1 Effects of goemetric structures....27
2.3.2 Effects of temperature...............30
2.4 Concluding remarks..............34
References.........................36
Chapter 3. Low-frequency excitation spectra in double-walled armchair carbon nanotubes
3.1 Introduction..........................38
3.2 Low-energy electronic structures.....................40
3.3 Electronic excitation spectra..............42
3.4 Summary................................52
References............................53
Chapter 4. Electronic structures of carbon nanotubes adsorbed on graphene
4.1 Introduction......................57
4.2 Tight-binding calculation...............59
4.3 Band structures................62
4.4 Summary.............................70
References............................71
Chapter 5. Low-frequency magnetooptical spectrum of bilayer Bernal graphene
5.1 Introduction.....................74
5.2 Theory..............................76
5.3 Landau structures in bilayer graphene......78
5.4 Bilayer optical excitations.............80
5.5 Summary....................86
References............................87
Chapter 6. Summary and future research......90

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Chapter 6
[1] Y. H. Ho, C. P. Chang, F. L. Shyu, C. W. Chiu, S. C. Chen and M. F. Lin, "Electronic and optical properties of double-walled armchair carbon nanotubes", Carbon 42, 3159-3167 (2004).
[2] S. C. Chen, I. Y. Chen, Y. H. Ho, and M. F. Lin, "Optical properties of BC3 nanotubes", J. Vac. Sci. Technol. B 24, 46-49 (2006).
[3] C. W. Chiu, Y. H. Ho, S. C. Chen, C. H. Lee, C. S. Lue, and M. F. Lin, "Electronic decay rates in semiconducting carbon nanotubes", Physica E 34, 658-661 (2006).
[4] Y. H. Ho, G. W. Ho, T. S. Li, and M. F. Lin, "Electronic excitations of double-walled armchair carbon nanotubes", Physica E 32, 569-572 (2006).
[5] S. J. Wu, Y. H. Ho, C. P. Chang, and M. F. Lin, "Electronic properties of armchair carbon nanotube array", Physica E 32, 581-584 (2006).
[6] G. W. Ho, Y. H. Ho, T. S. Li, C. P. Chang, and M. F. Lin, "Band structure and absorption spectrum of double-walled zigzag carbon nanotubes in an electric field", Carbon 44, 2323-2329 (2006).
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[1] Y. H. Ho, C. P. Chang, F. L. Shyu, C. W. Chiu, S. C. Chen and M. F. Lin (APS March Meeting 2004)"Magnetoelectronic structures of double-walled armchair carbon nanotubes", Bulletin of American Physical Society, Vol. 49, 247 (2004).
[2] Y. H. Ho, C. P. Chang, F. L. Shyu, C. W. Chiu, S. C. Chen and M. F. Lin, "Magnetoelectronic structures of double-walled armchair carbon nanotubes", Annual Meeting of the Physical Society of the ROC (2004). (Oral)
[3] Y. H. Ho, G. W. Ho, and M. F. Lin, "Band structures of double-walled carbon nanotubes", The 1st International Conference on One-Dimensional Nanomaterials (2005).
[4] S. C. Chen, I. Y. Chen, Y. H. Ho, and M. F. Lin, "Optical properties of BC3 nanotubes", The 1st International Conference on One-Dimensional Nanomaterials (2005).
[5] C. W. Chiu, Y. H. Ho, S. C. Chen, C. H. Lee, C. S. Lue, and M. F. Lin, "Electron decay rate in semiconducting carbon nanotubes", The 16th International Conference on the Electronic Properties of Two-Dimensional Systems (2005).
[6] Y. H. Ho, G. W. Ho, T. S. Li, and M. F. Lin, "Electronic Excitations of Double-Walled Armchair Carbon Nanotubes", The 12th International Conference on the Modulated Semiconductor Structures (2005).
[7] S. J. Wu, Y. H. Ho, C. P. Chang, and M. F. Lin, "Electronic Properties of Armchair Carbon Nanotube Array", The 12th International Conference on the Modulated Semiconductor Structures (2005).
[8] Y. H. Ho, Y. H. Lai, H. P. Lin, and M. F. Lin, "Effects of geometric structures and temperature on electronic properties of double-walled armchair carbon nanotubes", Annual Meeting of the Physical Society of the ROC (2006). (Oral)
[9] Y. H. Ho, G. W. Ho, C. P. Chang, and M. F. Lin (APS March06 Meeting) "Band structure and absorption spectrum of double-walled zigzag carbon nanotubes in an electric field", Bulletin of American Physical Society, Vol. 51, 583 (2006).
[10] C. W. Chiu, Y. H. Ho, F. L. Shyu, and M. F. Lin (APS March06 Meeting) "Electronic excitations and deexcitations in narrow-gap carbon nanotubes", Bulletin of American Physical Society, Vol. 51, 584 (2006).
[11] Y. H. Ho, G. W. Ho, T. S. Li, and M. F. Lin, "Loss spectra of double-walled armchair carbon nanotubes", Proceeding of the 4th International Conference on Quantum Engineering Science, P.10-P.14 (2006)
[12] C. H. Lee, Y. H. Ho, R. B. Chen, and M. F. Lin, "Electronic structures of finite double-walled carbon nanotubes", International Conference on Superlattices, Nano-structures, and Nano-devices (2006).
[13] C. H. Lee, Y. H. Ho, R. B. Chen, Y. C. Hsue, and M. F. Lin, "Electronic properties of finite double-walled carbon nanotubes under external fields", Annual Meeting of the Physical Society of the ROC (2007).
[14] H. P. Lin, Y. H. Ho, S. C. Chen, C. Y. Lin, and M. F. Lin, "Electronic structures of monolayer and AB-staked bilayer graphemes under uniform deformations", The 17th International Conference on the Electronic Properties of Two-Dimensional Systems (2007).
[15] P. L. Lai, S. C. Chen, Y. H. Ho, and M. F. Lin, "Electronic properties of single-walled carbon nanotubes under electric fields", The 13th International Conference on the Modulated Semiconductor Structures (2007).
[16] J. Y. Wu, J. H. Ho, Y. H. Lai, Y. H. Ho, and M. F. Lin, "The low-energy electronic structures of nanographite ribbons in modulated magnetic fields", The 13th International Conference on the Modulated Semiconductor Structures (2007).
[17] Y. H. Ho, H. P. Lin, and M. F. Lin, "Effects of geometric structures and temperature on electronic properties of double-walled armchair carbon nanotubes", The 18th European Conference on Diamond, Diamond-Like Materials, Carbon nanotubes, and Nitrides (2007).
[18] Y. H. Ho, C. P. Chang, and M. F. Lin (APS March08 Meeting) "Electronic properties of nanotube-graphene composite carbon systems", Bulletin of American Physical Society, P. 800 (2008). (Oral)
[19] S. C. Chen, T. S. Wang, Y. H. Ho, and M. F. Lin, "Magneto-electonic properties of graphene nanoribbons in the spatially modulated electric field", The 2nd Conference on New Diamond and Nano Carbons (May, 2008).
[20] S. H. Lee, G. J. Tian, S. B. Lin, Y. H. Ho, and M. F. Lin, "Low-energy electronic and optical properties of the AB-stacked bilayer graphene under uniform deformations", The 2nd Conference on New Diamond and Nano Carbons (May, 2008).
[21] Y. H. Ho, H. P. Lin, and M. F. Lin, "Electronic structures of carbon nanotubes adsorbed on graphene", The 2nd Conference on New Diamond and Nano Carbons (May, 2008).