利用廣義緊束縛模型，計算電子在不同石墨烯結構中的磁量子化現象。零磁場能帶與藍道能階有對應關係，波函數行為與幾何結構有對應關係。具特定對稱性結構的石墨烯藍道能階為四重簡併，AAB堆疊石墨烯因特殊的結構破壞其對稱性，結果為二重簡併，分別對應至不同特定位置的波函數。藍道能階隨磁場的變化行為特殊，第一群與第二群藍道能階有”反交叉”現象，藍道能階能量大小隨磁場變化震盪，震盪振幅對應零磁場能帶振幅，第三群藍道能階則無”反交叉”與”能帶震盪”現象。藍道能階對應的波函數分佈在特定位置，不同位置藍道能階隨磁場變化的行為不同。

This research is about magnetoelectric properties of AAB-stacked graphene. There are different electronic and optical properties in different stacking of graphene. The band structure and the Landau levels(LLs) could be used to analyse. General tight-binding method is used to calculate the band structure and the LLs. Tight-binding function satisfies periodic potentials in lattice. The band structure depends on the geometric properties, and the LLs depends on the band structure. AAB-stacked graphene has special properties because of the special geometric properties.

1. P. R. Wallace, Phys. Rev. 71, 622 (1947)
2. J. H. Ho, C. L. Lu, C. C. Hwang,C. P. Chang, and M. F. Lin, Phys. Rev. 74, 085406 (2006)
3. J.H. Ho, Y.H. Lai, Y.H. Chiu, M.F. Lin, Physica E 40 (2008) 1722-1725
4. C.P. Chang, C.L. Lu, F.L. Shyu, R.B. Chen, Y.K. Fang, M.F. Lin, Carbon 42 (2004) 2975-2980
5. Y. H. HO, J. Y. WU, Y. H. CHIU, J. WANG AND M. F. LIN, Phil, Trans. R. Soc. A (2010) 368,5445-5458
6. Saito, Physical Properties of Carbon Nanotubes, Imperial College Press, London , p.95 - 113 (1998)
7. Charles Kittel, Introduction to Solid State Physics, 8th Edition, John Wiley & Sons, Inc, U.S., (2004), p.232 – 235
8. J.H. Ho, Y.H. Lai, C.P. Chang , M.F. Lin, Diamond & Related Materials 18 (2009) 374–379
9. Y.H. Lai , C.P. Chang, J.H. Ho, C.H. Ho, M.F. Lin, Physics Letters A 372 (2008) 292–298
10. Chih-Wei Chiu, Szu-Chao Chen,Yuan-Cheng Huang,Feng-Lin Shyu and Ming-Fa Lin, APPLIED PHYSICS LETTERS 103, 041907 (2013)
11. Y. H. Ho, J. Y. Wu, Y. H. Chiu, J. Wang and M. F. Lin, Phil. Trans. R. Soc. A (2010) 368, 5445–5458
12. Pilkyung Moon, Mikito Koshino, PhysRevB.85.195458 (2012)