WKB estimate of bilayer graphene's magic twist angles
arXiv:2006.13292 · doi:10.1103/PhysRevLett.126.016404
Abstract
Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck's constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wavefunctions. We find zero energy solutions at a discrete set of values of the dimensionless Planck's constant, which we obtain analytically. Our analytic flat band twist angles correspond closely to those determined numerically in previous work.
7 pages, 6 figures, Comments are welcome
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Cited by in corpus (24)
- Graphene Bilayers with a Twist
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- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
- Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
- Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene
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- Heavy fermion representation for twisted bilayer graphene systems
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- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
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- Dynamical correlations and order in magic-angle twisted bilayer graphene
- Spectral characterization of magic angles in twisted bilayer graphene
- Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
- Electronic localization in small-angle twisted bilayer graphene
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- Dirac Fermion Cloning, Moir Flat Bands and Magic Lattice Constants in Epitaxial Monolayer Graphene
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- Moiré semiconductors on twisted bilayer dice lattice
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- Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski