在本篇論文中利用了緊束模型來研究一維單層奈米石墨帶在外加空間調制磁場下的光學性質和電子性質。外加磁場方向為垂直石墨帶，經由緊束模型計算出能帶。在費米能上會有部分平坦能帶和在其他地方的拋物線能帶，受到調制磁場影響使電子聚集在準藍道能階，並分裂出subbands。在吸收光譜中主要鋒和子鋒分別由能帶原始band-edge state和額外band-edge state所產生的，都會受到調制磁場的改變產生劇烈的變化。能帶上的變化可以反應在吸收光譜上，外加的磁場改變光譜鋒的位置、鋒的高度甚至產生新的鋒。這些光譜特徵鋒的變化可以在光學和傳輸實驗中被量測到。

The tight-binding model is utilized to study the optical properties and electronic properties of 1D graphene nanoribbons under the influence of spatially modulated magnetic fields. The spatially modulated magnetic field is perpendicular to the graphene plane,Energy band is calculated using the tight-binding model. They display the partial flat bands at the Fermi level and parabolic bands at others. Affected by spatially modulation magnetic fields , electrons are dragged into quasi-Landau levels, and QLL is going to separate into two subbands. The optical-absorption spectra exhibits the principal peaks and the subpeaks, respectively from the original band-edge state and the extra band-edge states. They all present drastic changes under the variation of magnetic field modulation. The features of optical-absorption spectra fully reflect the changes in band structure. The modulated magnetic field changes spectral peak position, alters peak height and even produces new peaks. The characteristic could be measured in optical and transport measurements.

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature 438, 197 (2005).
[3] Y. Zhang, Y. W. Tan, H.-L. Stormer, and P. Kim, Nature 438, 201 (2005).
[4] M. Y. Han, B. Özyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98, 206805 (2007).
[5] T. Tanaka, A. Tajima, R. Moriizumi, M. Hosoda, R. Ohno, E. Rokuta, C. Oshima, and S. Otani, Solid State Commun. 123, 33 (2002).
[6] C. P. Chang, Y. C. Huang, C. L. Lu, J. H. Ho, T. S. Li, and M. F. Lin, Carbon 44, 508 (2006).
[7] Y. C. Huang, C. P. Chang, and M. F. Lin, Nanotechnology 18, 495401 (2007).
[8] H. A. Carmona, A. K. Geim, A. Nogaret, P. C. Main, T. J. Foster, M. Henini, S. P. Beaumont, and M. G. Blamire, Phys. Rev. Lett. 74, 3009 (1995).
[9] P. D. Ye, D. Weiss, R. R. Gerhardts, M. Seeger, K. von Klitzing, K. Eberl, and H. Nickel, Phys. Rev. Lett. 74, 3013 (1995).
[10] S. Halm, F. Seifert, T. Kummell, G. Bacher, E. Schuster, W. Keune, J. Puls, and F. Henneberger, phys. stat. sol. (c) 3, 1122 (2006).
[11] J. C. Charlier, J. P. Michenaud, X. Gonze, and J. P. Vigneron, Phys. Rev. B 44, 237 (1991).
[12] M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996).

[13] Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe, and Y. Kaburagi, Phys. Rev. B 71, 193406 (2005).
[14] Y. Kobayashi, K. Fukui, and T. Enoki, Phys. Rev. B 73, 125415 (2006).
[15] Y. Niimi, T. Matsui, H. Kambara, K. Tagami, M. Tsukada, and H. Fukuyama, Phys. Rev. B 73, 085421 (2006).
[16] D. Tekleab, R. Czerw, and D. L. Carroll, Appl. Phys. Lett. 76, 3594 (2000).
[17] A. I. Onipko, K.-F. Berggren, Yu. O. Klymenko, L. I. Malysheva, J. J. W. M. Rosink, L. J. Geerligs, E. van der Drift, and S. Radelaar, Phys. Rev. B 61, 011118 (2000).
[18] L. M. Malard, J. Nilsson, D. C. Elias, J. C. Brant, F. Plentz, E. S. Alves, A. H. Castro Neto, and M. A. Pimenta, Phys. Rev. B 76, 201401 (2007).
[19] A. Jorio, G. S. Filho, G. Dresselhaus, M. S. Dresselhaus, R. Saito, J. H. Hafner, C. M. Lieber, F. M. Matinaga, M. S. Dantas, and M. A. Pimenta, Phys. Rev. B 63, 245416 (2001).
[20] M. Koshino and T. Ando, Phys. Rev. B 77, 115313 (2008).
[21] M. J. O’Connell, S. M. Bachilo, C. B. Huffman, V. C. Moore, M. S. Strano, E. H. Haroz, K. L. Rialon, P. J. Boul, H. W. Noon, C. Kittrell, J. Ma, R. H. Hauge, R. B. Weisman, and R. E. Smalley, Science 297, 593 (2002).