Graphene in a periodically alternating magnetic field: An unusual quantization of the anomalous Hall effect

M. Taillefumier, V. K. Dugaev, B. Canals, C. Lacroix, and P. Bruno
Phys. Rev. B 84, 085427 – Published 25 August 2011

Abstract

We study the energy spectrum and electronic properties of graphene in a periodic magnetic field of zero average with a symmetry of triangular lattice. The periodic field leads to the formation of a set of minibands separated by gaps, which can be manipulated by an external field. The Berry phase, related to the motion of electrons in k space, and the corresponding Chern numbers characterizing the topology of the energy bands are calculated analytically and numerically. In this connection, we discuss the anomalous Hall effect in the insulating state, when the Fermi level is located in the minigap. The results of calculations show that in the model of a gapless Dirac spectrum of graphene, the anomalous Hall effect can be treated as a sum of fractional quantum numbers, related to the nonequivalent Dirac points.

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  • Received 3 August 2011

DOI:https://doi.org/10.1103/PhysRevB.84.085427

©2011 American Physical Society

Authors & Affiliations

M. Taillefumier1, V. K. Dugaev2,3,4, B. Canals4, C. Lacroix4, and P. Bruno5

  • 1Department of Physics, University of Oslo, N-0316 Oslo, Norway
  • 2Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, PL-35-959 Rzeszów, Poland
  • 3Department of Physics and CFIF, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, P-1049-001 Lisbon, Portugal
  • 4Institut Néel, CNRS/UJF, 25 avenue des Martyrs, BP 166, F-38042 Grenoble, Cedex 09, France
  • 5European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, Cedex, France

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Issue

Vol. 84, Iss. 8 — 15 August 2011

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