Continuum Model of the Twisted Bilayer

Abstract

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 $\theta \to 0$, 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}.

13 pages, 17 figures

References in corpus (13)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Unconventional Integer Quantum Hall effect in graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Numerical studies of confined states in rotated bilayers of graphene
• Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
• Reduction of Fermi velocity in folded graphene observed by resonance Raman spectroscopy
• Minimal conductivity in bilayer graphene
• Dirac and Normal Fermions in Graphite and Graphene: Implications to the Quantum Hall Effect

Cited by in corpus (6)

• Colloquium: Graphene spectroscopy
• Optical Conductivity of Twisted Bilayer Graphene
• Terahertz conductivity of twisted bilayer graphene
• Electronic Properties of Twisted Trilayer Graphene
• The Coexistence of van Hove Singularities and Superlattice Dirac Points in a Slightly Twisted Graphene Bilayer
• The electronic band structures and optical absorption spectra for incommensurate twisted few-layers graphene