Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models |
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Authors: | J N Fuchs F Piéchon M O Goerbig and G Montambaux |
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Institution: | (1) IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Sachsen, Germany |
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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 (h/2p)\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. |
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Keywords: | |
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