在這篇論文中我們研究少層石墨的低能藍道能階。藍道能階的分佈強烈的依賴磁場強度、堆疊的層數和堆疊的結構。層間原子的交互作用使低能處產生了更多的藍道能階而且藍道能階不以費米能做對稱。雙層AA堆疊石墨的低藍道能階光譜無法像雙層AB堆疊石墨有簡單的關係式可以計算。然而雙層AA堆疊石墨低能的藍道能階，根據兩群的等效量子數 和 可以分類成兩組藍道能階，而兩組藍道能階能量近似與等效量子數和磁場強度有依賴性。三層AA堆疊石墨則有三組藍道能階，藉由觀看載子分佈密度可以知道各別在外層和中間層的分佈情形。由於外部兩層所受的化學環境相同，載子分佈密度會有相同的表現，而中間層的化學環境與外層不同，因此載子分佈密度與外部兩層有不同的表現。這些結果也幫助了解層間交互作用間的藕合如何影響低能的電磁特性，而且可用來分析光學光譜實驗。

In this paper,we investigate the low energy landau levels (LLs) in few layer graphene.The LL distribution strongly depends on the magnetic field strength, the layer number,and the stacking structure. The interlayer atomic interations lead to more low LLs and the asymmetry LLs about the zero Fermi energy. For AA-stacked bilayer graphene, the low lying LLspectrum cannot be accounted by a simple relation as that was made in AB-stacked bilayer graphene.However, it can be categorized into two groups of LLs according to the two sets of effective quantum numbers and . The two groups of LLs show the similar dependence on the quantum number and field strength. For AA-stacked trilayer graphene, there are three groups of LLs. By examining the carrier density distribution, we know that they are attributed to the outmost layers and the middle layer respectively.
These results are helpful to understand how the interlayer couplings affect the low-energy magnetoelectronic properties and could be used to analyze the optical experiments.

1. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306 (2004) 666.
2. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438 (2005) 197.
3. C. Berger, Z.M. Song, T.B. Li, X.B. Li, A.Y. Ogbazghi, R. Feng, Z.T. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, J. Phys. Chem. B 108(2004) 19912.
4. J. Nilsson, A.H.C. Neto, F. Guinea, N.M.R. Peres, Phys. Rev. Lett. 97 (2006) 266801.
5. E. McCann, Phys. Rev. B 74 (2006) 161403.
6. C.L. Lu, C.P. Chang, Y.C. Huang, J.M. Lu, C.C. Hwang, M.F. Lin, J. Phys.: Condens. Matter 18 (2006) 5849.
7. F. Guinea, A.H.C. Neto, N.M.R. Peres, Phys. Rev. B 73 (2006) 245426.
8. N.M.R. Peres, F. Guinea, A.H.C. Neto, Ann. Phys. 321 (2006) 1559.
9. B. Partoens, F.M. Peeters, Phys. Rev. B 74 (2006) 075404.
10. X.-F. Wang, T. Chakraborty, Phys. Rev. B 75 (2007) 041404.
11. S.D. Sarma, E.H. Hwang, W.-K. Tse, Phys. Rev. B 75 (2007) 121406.
12. A.H.C. Neto, F. Guinea, Phys. Rev. B 75 (2007) 045404.
13. J.H. Ho, C.L. Lu, C.C. Hwang, C.P. Chang, M.F. Lin, Phys. Rev. B 74 (2006) 085406.
14. A. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nature Phys. 3 (2007) 36.
15. V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, J. Phys.: Condens. Matter 19 (2007) 026222.
16. A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, A.K. Geim, Phys. Rev. Lett. 97(2006) 187401.
17. D.S.L. Abergel, V.I. Fal’ko, Phys. Rev. B 75 (2007) 155430.
18. C.L. Lu, H.L. Lin, C.C. Hwang, J. Wang, C.P. Chang, M.F. Lin, Appl. Phys. Lett. 89 (2006) 221910(3).
19. K.S. Novoselov, E. McCann, S.V. Morozov, V.I. Fal’ko, M.I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, A.K. Geim, Nature Phys. 2 (2006) 177.
20. V.P. Gusynin, S.G. Sharapov, Phys. Rev. B 73 (2006) 245411.
21. V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95 (2005) 146801.
22. V.P. Gusynin, V.A. Miransky, S.G. Sharapov, I.A. Shovkovy, Phys. Rev. B 74 (2006) 195429.
23. P.R. Wallace, Phys. Rev. 71 (1947) 622.
24. Y. Zheng, T. Ando, Phys. Rev. B 65 (2002) 245420.
25. J.H. Ho, Y.H. Lai, S.J. Tsai, J.S. Hwang, C.P. Chang, M.F. Lin, J. Phys. Soc. Jpn. 75 (2006) 114703.
26. J.H. Ho, Y.H. Lai, C.L. Lu, J.S. Hwang, C.P. Chang, M.F. Lin, Phys. Lett. A 359 (2006) 70.
27. C.P. Chang, C.L. Lu, F.L. Shyu, R.B. Chen, Y.K. Fang, M.F. Lin, Carbon 42 (2004) 2975.
28. J.H. Ho, Y.H. Lai, Y.H. Chiu, M.F. Lin, arXiv: 0706.0078 [cond-mat], unpublished.
29. J.C. Charlier, J.-P. Michenaud, X. Gonze, Phys. Rev. B 46 (1992) 4531.