Abstract

The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99,\n256802, 2007) is extended to include all types of commensurate structures. The\nessential ingredient of the model, the Fourier components of the spatially\nmodulated hopping amplitudes, can be calculated analytically, for any type of\ncommensurate structures in the low twist angle limit. We show that the Fourier\ncomponents that could give rise to a gap in the SE-even structures discussed by\nMele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the\namplitudes that saturate to finite values, as $\\theta\\to0$, ensure that all low\nangle structures share essentially the same physics. We extend our previous\ncalculations beyond the validity of perturbation theory, to discuss the\ndisappearance of Dirac cone structure at angles below 1^{\\circ}.\n

Keywords

Bilayer grapheneGrapheneMaterials scienceBilayerCondensed matter physicsNanotechnologyPhysicsChemistryMembrane

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Year
2012
Type
article
Volume
86
Issue
15
Citations
581
Access
Closed

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J. M. B. Lopes dos Santos, N. M. R. Peres, A. H. Castro Neto (2012). Continuum model of the twisted graphene bilayer. Physical Review B , 86 (15) . https://doi.org/10.1103/physrevb.86.155449

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DOI
10.1103/physrevb.86.155449