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arXiv · 1203.2605

Magnetic spectrum of trigonally warped bilayer graphene - semiclassical analysis, zero modes, and topological winding numbers

R. de Gail·M. O. Goerbig·G. Montambaux
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Abstract

We investigate the fine structure in the energy spectrum of bilayer graphene in the presence of various stacking defaults, such as a translational or rotational mismatch. This fine structure consists of four Dirac points that move away from their original positions as a consequence of the mismatch and eventually merge in various manners. The different types of merging are described in terms of topological invariants (winding numbers) that determine the Landau-level spectrum in the presence of a magnetic field as well as the degeneracy of the levels. The Landau-level spectrum is, within a wide parameter range, well described by a semiclassical treatment that makes use of topological winding numbers. However, the latter need to be redefined at zero energy in the high-magnetic-field limit as well as in the vicinity of saddle points in the zero-field dispersion relation.

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R. de Gail, M. O. Goerbig, G. Montambaux. 2012-03-10. Magnetic spectrum of trigonally warped bilayer graphene - semiclassical analysis, zero modes, and topological winding numbers. https://doi.org/10.1103/physrevb.86.045407

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