The Peierls Hamiltonian band matrix is developed to investigate magnetoelectronic properties of a bilayer Bernal graphene. A uniform perpendicular magnetic field creates many dispersionless Landau levels (LLs) at low and high energies and some oscillatory LLs at moderate energy. State degeneracy of the low LLs is two times as much as that of the high LLs. Wave functions and state energies are dominated by the interlayer atomic interactions and field strength (B0). The former induce two groups of LLs, more low LLs, the asymmetric energy spectrum about the Fermi level, and the change of level spacing. Two sets of effective quantum numbers, neff 1 's and neff 2 's, are equired to characterize all the wave functions. They are determined by the strongest oscillation modes of the dominant carrier densities; furthermore, they rely on the specific interlayer atomic hoppings. The dependence of the quite low Landau-level energies on B0 and neff 1 is approximately linear. An energy gap is produced by the magnetic field and interlayer atomic hoppings. Eg grows with the increasing field strength, while it is reduced by the Zeeman effect. The main features of magnetoelectronic structures are directly reflected in density of states. The predicted electronic properties could be verified by the experimental measurements on absorption spectra and transport properties.

Reference
[1] M. S. Dresselhaus and G. Dresselhaus, Adv. Phys. 30, 139 (1981).

[2] D. E. Soule, Phys. Rev. 112, 698 (1958).

[3] J. K. Galt, W. A. Yager, and H. W. Jr. Dail, Phys. Rev. 103, 1586 (1956).

[4] T. Matsui, H. Kambara, Y. Niimi, K. Tagami, M. Tsukada, and Hiroshi Fukuyama, Phys. Rev. Lett. 94, 226403 (2005).

[5] G. Li and E. Y. Andrei, Nat. Phys. 3, 623 (2007).

[6] P. R. Wallace, Phys. Rev. 71, 622 (1947).

[7] J. W. McClure, Phys. Rev. 104, 666 (1956).

[8] J. C. Chailier, J. -P. Michenaud, X. Gonze, Phys. Rev. B 46, 4531 (1992).

[9] J. C. Chailier, J. -P. Michenaud, X. Gonze, J. -P. Vigneron, Phys. Rev. B 44, 13237 (1991).

[10] F. L. Shyu and M. F. Lin, J. Phys. Soc. Jpn. 69, 3781 (2000).

[11] C. P. Chang, C. L. Lu, F. L. Shyu, R. B. Chen, Y. C. Huang, and M. F. Lin, Carbon 43, 1424 (2005).

[12] 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).

[13] 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).

[14] 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, and W. A. de Heer, J. Phys. Chem. B 108, 19912 (2004).

[15] C. Berger, Z. M. Song, T. B. Li, X. B. Li, X. Wu, N. Brown, C. Naud, D. Mayou, A. N. Marchenkov, and E. H. Conrad et al., Science 306, 1191 (2006).

[16] Y. Zheng and T. Ando, Phys. Rev. B 65, 245420 (2002).

[17] E. McCann, Phys. Rev. B 74, 161403 (2006).

[18] C. L. Lu, C. P. Chang, Y. C. Huang, J. M. Lu, C. C. Hwang, and M. F. Lin, Journal of Physics: Condensed Matter 18, 5849 (2006).

[19] F. Guinea, A. H. C. Neto, and N. M. R. Peres, Phys. Rev. B 73, 245426 (2006).

[20] E. McCann, K. Kechedzhi, V. I. Falko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006).

[21] B. Partoens and F. M. Peeters, Phys. Rev. B 74, 075404 (2006).

[22] M. Koshino and T. Ando, Phys. Rev. B 76, 085425 (2007)

[23] C. L. Lu, C. P. Chang, J. H. Ho, C. C. Tsai, and M. F. Lin, Physica E 32, 585 (2006).

[24] J. H. Ho, Y. H. Lai, S. J. Tsai, J. S. Hwang, C. P. Chang, and M. F. Lin, J. Phys. Soc. Jpn. 75, 114703 (2006).

[25] E. McCann and V. I. Fal'ko, Phys. Rev. Lett. 96, 086805 (2006).

[26] J. Milton Pereira, F. M. Peeters, and P. Vasilopoulos, Phys. Rev. B 76, 115419 (2007).

[27] N. Nemec and G. Cuniberti, Phys. Rev. B 75, 201404 (2007).

[28] J. H. Ho, Y. H. Lai, Y. H. Chiu, and M. F. Lin, arXiv:0706.0078v1 (unpublished).

[29] Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005).

[30] K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, and A. K. Geim, Science 315, 1379 (2007).

[31] K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal'ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, Nat. Phys. 2, 177 (2006).

[32] V. P. Gusynin and S. G. Sharapov, Phys. Rev. B 73, 245411 (2006).

[33] V. P. Gusynin, V. A. Miransky, S. G. Sharapov, and I. A. Shovkovy, Phys. Rev. B 74, 195429 (2006).

[34] M. Koshino and T. Ando, Phys. Rev. B 73, 245403 (2006).

[35] M. L. Sadowski, G. Martinex, and M. Potemski, C. Berger, and W. A. de Heer, Phys. Rev. Lett. 97, 266405 (2006).

[36] D. S. L. Abergel and Vladimir I. Fal'ko, Phys. Rev. B 75, 155430 (2007).

[37] R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, Phys. Rev. B 76, 081406 (2007).

[38] D. S. L. Abergel, A. Russell, and Vladimir I. Fal'ko, Appl. Phys. Lett. 91, 063125 (2007).

[39] C. L. Lu, C. P. Chang, Y. C. Huang, R. B. Chen, and M. F. Lin, Phys. Rev. B 73, 144427 (2006).

[40] C. L. Lu, H. L. Lin, C. C. Hwang, J. Wang, C. P. Chang, and M. F. Lin, Appl. Phys. Lett. 89, 221910 (2006).

[41] O. L. Berman, Y. E. Lozovik, and G. Gumbs, arXiv:0706.0244 (unpublished).

[42] X. -F. Wang and T. Chakraborty, Phys. Rev. B 75, 041404 (2007)

[43] X. -F. Wang and T. Chakraborty, Phys. Rev. B 75, 033408 (2007)

[44] J. H. Ho, C. P. Chang, and M. F. Lin, Phys. Lett. A 352, 446 (2006).

[45] J. H. Ho, C. P. Chang, R. B. Chen, and M. F. Lin, Phys. Lett. A 357, 401 (2006).

[46] J. H. Ho, C. L. Lu, C. C. Hwang, C. P. Chang, and M. F. Lin, Phys. Rev. B 74, 085406 (2006).

[47] M. F. Lin and F. L. Shyu, J. Phys. Soc. Jpn. 69, 609 (2000)

[48] M. F. Lin and K. W. -K. Shung, Phys. Rev. B 52, 8423 (1995).