J. M. B. Lopes dos Santos, N. M. R. Peres, A. H. Castro Neto
The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99,
256802, 2007) is extended to include all types of commensurate structures. The
essential ingredient of the model, the Fourier components of the spatially
modulated hopping amplitudes, can be calculated analytically, for any type of
commensurate structures in the low twist angle limit. We show that the Fourier
components that could give rise to a gap in the SE-even structures discussed by
Mele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the
amplitudes that saturate to finite values, as $\theta\to0$, ensure that all low
angle structures share essentially the same physics. We extend our previous
calculations beyond the validity of perturbation theory, to discuss the
disappearance of Dirac cone structure at angles below 1^{\circ}.
View original:
http://arxiv.org/abs/1202.1088
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