General continuum model for twisted bilayer graphene and arbitrary smooth deformations

Abstract

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

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• Floquet engineering of twisted double bilayer graphene
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• Strained Bilayer Graphene, Emergent Energy Scales, and Moire Gravity
• Theory of polarization textures in crystal supercells
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• Designer Meron Lattice on the Surface of a Topological Insulator
• Duality between atomic configurations and Bloch states in twistronic materials
• Multi-layered atomic relaxation in van der Waals heterostructures
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• Nematic insulator at charge neutrality in twisted bilayer graphene
• Josephson effects in twisted nodal superconductors
• Extrinsic Mechanisms of Phonon Magnetic Moment
• A Generic Topological Criterion for Flat Bands in Two Dimensions
• Anderson's theorem for correlated insulating states in twisted bilayer graphene
• Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers
• Magnon bands in twisted bilayer honeycomb quantum magnets
• Polarization textures in crystal supercells with topological bands
• Fractal non-Fermi liquids from moiré-Hofstadter phonons
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• Localizing Transitions via Interaction-Induced Flat Bands
• Review of the tight-binding method applicable to the properties of moiré superlattices
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
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• Moiré magnetism in a bilayer Ising model
• Charged moiré phonons in twisted bilayer graphene
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• Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene