Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene

Abstract

The recently realized bilayer graphene system with a twist angle of $30^{\circ }$ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We find that the electronic spectrum consists of resonant states labeled by 12-fold quantized angular momentum, together with the extended relativistic states. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. We also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. The theoretical method introduced here is applicable to a broad class of "extrinsic quasicrystals" composed of a pair of two-dimensional crystals overlaid on top of the other with incommensurate configurations.

9 pages, 6 figures

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Cited by in corpus (48)

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• Emergent Localization in Dodecagonal Bilayer Quasicrystals
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• Twistronics in graphene-based van der Waals structures
• Quantum many-body topology of quasicrystals
• Theory of polar domains in moiré heterostructures
• Charge 4e superconductivity and chiral metal in the $45^{\circ }$-twisted bilayer cuprates and similar bilayers
• Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order
• Moiré superlattice effects and band structure evolution in near-30-degree twisted bilayer graphene
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
• Topological charge pumping in quasiperiodic systems characterized by Bott index
• Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• Quasiperiodic pairing in graphene quasicrystals
• Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
• Built-in Bernal gap in large-angle-twisted monolayer-bilayer graphene
• Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist
• Quasicrystalline 30${}^{\circ }$ twisted bilayer graphene: Fractal patterns and electronic localization properties
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Band structure and band topology in twisted homotrilayer transition metal dichalcogenides
• Emergence of flat bands in the quasicrystal limit of boron nitride twisted bilayers
• Hidden hyperspace geometry and long-distance quantum coupling
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Moiré fractals in twisted graphene layers
• Moiré plane wave expansion model for scanning tunneling microscopy simulations of incommensurate two-dimensional materials
• Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: application to electronic structure and optical responses
• Gap labeling theorem for multilayer thin film heterostructures
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Construction of optimized tight-binding models using \textit{ab initio} Hamiltonian: Application to monolayer $2H$-transition metal dichalcogenides
• Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
• Energy Spectrum Theory of Incommensurate Systems
• Trigonal Quasicrystalline States in $30^{\circ }$ Rotated Double Moiré Superlattices
• Electronic Observables for Relaxed Bilayer 2D Heterostructures in Momentum Space
• Symmetry-directed electronic and optical properties in a two-dimensional square-lattice ZnPc-MOF
• Raman Characterization of Two-Dimensional Quasiperiodic Antiferromagnets on Various Lattices: Spin-Orbit Mechanism
• Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene
• Insulating Electronic States Near the Dirac Point Arising from Twisted Stacking and Curvature in 3D Nanoporous Graphene
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions
• Efficient algorithm for simulating particles in real quasiperiodic environments
• Electronic Reconstruction at the Quasicrystal-Moiré Crossover in Twisted Bilayer Graphene