https://doi.org/10.1140/epjb/e2010-00259-2
Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, 91405 Orsay, France
Corresponding author: a fuchs@lps.u-psud.fr
Received:
8
July
2010
Published online:
13
September
2010
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 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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2010