Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-06-29
Eur. Phys. J. B 77, 351 (2010)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
15 pages, 6 figures, submitted to EPJB
Scientific paper
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.
Fuchs Jean-Noël
Goerbig Mark O.
Montambaux Gilles
Piéchon Frédéric
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