Skip to main content
Log in

Disorder and localization of electrons in bilayer graphene

  • Mesoscopic and Nanoscale Systems
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We investigate localization behavior of electron states in bilayer graphene formed with the Bernal stacking in the presence of various types of disorder (site-energy, in-plane hopping and inter-plane hopping) by the use of the transfer matrix method. It is found that all the states are localized at various kinds of disorder (site-energy, in-plane hopping and inter-plane hopping) except that in the case of inter-plane-hopping disorder the states at the zero energy are critical. The implications of the results are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • J.W. McClure, Phys. Rev. 108, 666 (1956)

    Google Scholar 

  • G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984)

    Google Scholar 

  • F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)

  • D.V. Khveshchenko, Phys. Rev. Lett. 87, 206401 (2001)

    Google Scholar 

  • V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005)

    Google Scholar 

  • K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)

  • C. Berger, Z. Song, T. Li, S. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, Phys. Chem. B 108, 19912 (2004)

    Google Scholar 

  • K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature (London)438, 197 (2005)

    Google Scholar 

  • Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Nature (London) 438, 201 (2005)

    Google Scholar 

  • Y. Zhang, Z. Jiang, J.P. Small, M.S. Purewal, Y.-W. Tan, M. Fazlollahi, J.D. Chudow, J.A. Jaszczak, H.L. Stormer, P. Kim, Phys. Rev. Lett. 96, 136806 (2006)

    Google Scholar 

  • K. Ziegler, Phys. Rev. Lett. 97, 266802 (2006)

    Google Scholar 

  • K. Nomura, A.H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006)

    Google Scholar 

  • D.N. Sheng, L. Sheng, Z.Y. Weng, Phys. Rev. B 73, 233406 (2006)

    Google Scholar 

  • A. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nat. Phys. 3, 36 (2007)

    Google Scholar 

  • W.-K. Tse, S. Das Sarma, Phys. Rev. Lett. 99, 236802 (2007)

    Google Scholar 

  • S.V. Kravchenko, G.V. Kravchenko, J.E. Furneaux, V.M. Pudalov, M. D’Iorio, Phys. Rev. B 50, 8039 (1994)

    Google Scholar 

  • C. Castellani, C.D. Castro, P.A. Lee, M. Ma, Phys. Rev. B 30, 527 (1984)

    Google Scholar 

  • S.-Jie Xiong, G.-Ping Zhang, Phys. Rev. B 68, 174201 (2003)

    Google Scholar 

  • E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)

    Google Scholar 

  • P.W. Anderson, Phys. Rev. 109, 1429 (1958)

    Google Scholar 

  • S.-Jie Xiong, Y. Xiong, Phys. Rev. B 76, 214204 (2007)

    Google Scholar 

  • P.R. Wallace, Phys. Rev. 71, 622 (1947)

    Google Scholar 

  • E. McCann, V.I. Fal’ko, Phys. Rev. Lett. 96, 086805 (2006)

    Google Scholar 

  • Y. Zheng, T. Ando, Phys. Rev. B 65, 245420 (2002)

    Google Scholar 

  • V.P. Gusynin, S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005)

    Google Scholar 

  • M. Nakamura, L. Hirasawa, Phys. Rev. B 77, 045429 (2008)

    Google Scholar 

  • J.W. McClure, Phys. Rev. 108, 612 (1957)

    Google Scholar 

  • J.C. Slonczewski, P.R. Weiss, Phys. Rev. 109, 272 (1958)

    Google Scholar 

  • W.W. Toy et al., Phys. Rev. B 15, 4077 (1977)

  • A. Misu, E. Mendez, M.S. Dresslhaus, J. Phys. Soc. Jpn 47, 199 (1979)

    Google Scholar 

  • C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)

    Google Scholar 

  • Y. Imry, Europhys. Lett. 1, 249 (1986)

  • J.L. Pichard, G. Andre, Europhys. Lett. 2, 477 (1986)

    Google Scholar 

  • A. MacKinnon, B. Kramer, Phys. Rev. Lett. 47, 1546 (1981)

    Google Scholar 

  • A. MacKinnon, B. Kramer, Z. Phys. B: Condens. Matter 53, 1 (1983)

  • A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, e-print arXiv:0709.1163v2

  • M. Kohmoto, Y. Hasegawa, Phys. Rev. B 76, 205402 (2007)

    Google Scholar 

  • L. Brey, H.A. Fertig, Phys. Rev. B 73, 235411 (2007)

    Google Scholar 

  • D.A. Areshkin, D. Gunlycke, C.T. White, Nano Lett. 7, 204 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Y.-X. Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, YX., Xiong, SJ. Disorder and localization of electrons in bilayer graphene. Eur. Phys. J. B 67, 63–69 (2009). https://doi.org/10.1140/epjb/e2009-00011-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2009-00011-1

PACS

Navigation