Band collapse and the quantum Hall effect in graphene

B. Andrei Bernevig, Taylor L. Hughes, Shou Cheng Zhang, Han Dong Chen, Congjun Wu

Research output: Contribution to journalArticle


The recent quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a. phenomenon which we call band collapse. As a corollary, for low magnetic fields, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.

Original languageEnglish (US)
Pages (from-to)3257-3278
Number of pages22
JournalInternational Journal of Modern Physics B
Issue number22
StatePublished - Sep 10 2006
Externally publishedYes


  • Edge states
  • Graphene
  • Quantum Hall effect
  • Tight-binding

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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