Skip to main content
SpringerLink
Log in

Edge physics of graphene in the quantum Hall regime

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract.

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • K.S. Novoselov et al., Science 306, 666 (2004)

  • For recent reviews, see T. Ando, J. Phys. Soc. Jpn. 74, 777 (2005); M.A.H. Vozmediano, M.P. López-Sancho, T. Stauber, F. Guinea, Phys. Rev. B 72, 155121 (2006); and references therein

  • K.S. Novoselov et al., Nature 438, 197 (2005)

  • Y. Zhang et al., Nature 438, 201 (2005)

  • Y. Zheng, T. Ando, Phys. Rev. B 65, 245420 (2002); V.P. Gusynin, S.G. Shaparov, Phys. Rev. Lett. 95, 146801 (2005); N.M.R. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 73, 125411 (2006)

  • For a review, see article by C.L. Kane, M.P.A. Fisher, Perspectives in Quantum Hall Effects, edited by S. Das Sarma, A. Pinczuk (Wiley, New York, 1997), pp. 109–160

  • L. Brey, H.A. Fertig, Phys. Rev. B 73, 195408 (2006)

    Google Scholar 

  • L. Brey, Bull. Am. Phys. Soc. 51, 459 (2006); D.A. Abanin et al., Phys. Rev. Lett. 96, 176803 (2006)

  • For a review, see article by S.M. Girvin, A.H. MacDonald, Perspectives in Quantum Hall Effects, edited by S. Das Sarma, A. Pinczuk (Wiley, New York, 1997), pp. 161–224

  • H.A. Fertig, L. Brey, Phys. Rev. Lett. 97, 116805 (2006)

    Google Scholar 

  • V.I. Fal'ko, S.V. Iordanskii, Phys. Rev. Lett. 82, 402 (1999)

    Google Scholar 

  • T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, New York, 2004)

  • B.I. Halperin, Phys. Rev. B 25, 2185 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Indiana University, 47405, Bloomington, Indiana, USA

    H. A. Fertig

  2. Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, 28049, Madrid, Spain

    L. Brey

Authors
  1. H. A. Fertig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Brey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. A. Fertig.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fertig, H., Brey, L. Edge physics of graphene in the quantum Hall regime. Eur. Phys. J. Spec. Top. 148, 143–150 (2007). https://doi.org/10.1140/epjst/e2007-00234-4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2007-00234-4

Keywords

Search

Navigation