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The European Physical Journal Special Topics

, Volume 148, Issue 1, pp 143–150 | Cite as

Edge physics of graphene in the quantum Hall regime

  • H. A. FertigEmail author
  • L. Brey
Article
  • 110 Downloads

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.

Keywords

Domain Wall Dirac Equation European Physical Journal Special Topic Landau Level Edge State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. K.S. Novoselov et al., Science 306, 666 (2004) Google Scholar
  2. 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 Google Scholar
  3. K.S. Novoselov et al., Nature 438, 197 (2005) Google Scholar
  4. Y. Zhang et al., Nature 438, 201 (2005) Google Scholar
  5. 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) Google Scholar
  6. 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 Google Scholar
  7. L. Brey, H.A. Fertig, Phys. Rev. B 73, 195408 (2006) Google Scholar
  8. L. Brey, Bull. Am. Phys. Soc. 51, 459 (2006); D.A. Abanin et al., Phys. Rev. Lett. 96, 176803 (2006) Google Scholar
  9. 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 Google Scholar
  10. H.A. Fertig, L. Brey, Phys. Rev. Lett. 97, 116805 (2006) Google Scholar
  11. V.I. Fal'ko, S.V. Iordanskii, Phys. Rev. Lett. 82, 402 (1999) Google Scholar
  12. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, New York, 2004) Google Scholar
  13. B.I. Halperin, Phys. Rev. B 25, 2185 (1982) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of PhysicsIndiana UniversityBloomingtonUSA
  2. 2.Instituto de Ciencia de Materiales de Madrid (CSIC)MadridSpain

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