The quantum Hall effect in graphene from a lattice perspective

Bogdan Andrei Bernevig, Taylor L. Hughes, Shou Cheng Zhang

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The recent quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall 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 continuum Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the bulk 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 field, graphene will exhibit two qualitatively different quantum Hall effects (QHEs): 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)20-26
Number of pages7
JournalSolid State Communications
Volume143
Issue number1-2
DOIs
StatePublished - Jul 1 2007

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Condensed Matter Physics
  • Materials Chemistry

Keywords

  • A. Graphene
  • D. Edge states
  • D. Quantum Hall effect

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