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The European Physical Journal B

, Volume 77, Issue 3, pp 351–362 | Cite as

Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models

  • J. N. FuchsEmail author
  • F. Piéchon
  • M. O. Goerbig
  • G. Montambaux
Solid State and Materials

Abstract.

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects – such as Berry phase and Maslov index – occurring at order \(\hbar\) in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase – which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands – acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the “k-dependent Hamiltonian” H(k), where k is the Bloch wavevector.

Keywords

Boron Nitride Landau Level Dirac Point Berry Phase Maslov Index 
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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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • J. N. Fuchs
    • 1
    Email author
  • F. Piéchon
    • 1
  • M. O. Goerbig
    • 1
  • G. Montambaux
    • 1
  1. 1.Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502OrsayFrance

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