Minimum model for the electronic structure of twisted bilayer graphene and related structures

Abstract

We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at $E_F$ flatten without overlap and two gaps open, one above and one below $E_F$. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.

arXiv comment5 pages, 3 figures

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• Magic of high order van Hove singularity
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• Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene
• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Disorder in Twisted Bilayer Graphene
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Is Twisted Bilayer Graphene Stable under Shear?
• Pressure induced gap modulation and topological transitions in twisted bilayer and double bilayer graphene
• Twistronics in graphene-based van der Waals structures
• Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides
• Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
• Harmonic Fingerprint of Unconventional Superconductivity in Twisted Bilayer Graphene
• Constrained Random Phase Approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene
• High transmission in twisted bilayer graphene with angle disorder
• $\text{Ab initio}$ four-band Wannier tight-binding model for generic twisted graphene systems
• Junctions and superconducting symmetry in twisted bilayer graphene
• Generalized Peierls substitution for the tight-binding model of twisted multilayer graphene in a magnetic field
• Electronic structure of carbon nanotubes on graphene substrates
• Determination of interatomic coupling between two-dimensional crystals using angle-resolved photoemission spectroscopy
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Designing Moire Patterns by Shearing
• Electron-hole superfluidity controlled by a periodic potential
• Renormalized Magic Angles in Asymmetric Twisted Graphene Multilayers
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors
• Magic distances in twisted bilayer graphene
• Impact of vacancies on twisted bilayer graphene quantum point contacts
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields