A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

Abstract

The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of $s{p}^2$ carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and twisted bilayer graphene. Subsequently, we illuminate the origin of flat bands in twisted bilayer graphene at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of twisted bilayer graphene not covered by this review but may readily be approached with the help of this primer.

arXiv commentTo be published as topical review in Journal of Physics: Condensed Mater ( Accepted Manuscript is available online)

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Cited by in corpus (7)

• Twisted bilayer graphene revisited: minimal two-band model for low-energy bands
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Moiré fractals in twisted graphene layers
• Photon absorption in twisted bilayer graphene
• Electronic analogue of Fourier optics with mass-less Dirac fermions scattered by quantum dot lattice
• Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene
• Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability