Continuum Model of the Twisted Bilayer

Abstract

The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99, 256802, 2007) is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically, for any type of commensurate structures in the low twist angle limit. We show that the Fourier components that could give rise to a gap in the SE-even structures discussed by Mele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the amplitudes that saturate to finite values, as $\theta \to 0$, ensure that all low angle structures share essentially the same physics. We extend our previous calculations beyond the validity of perturbation theory, to discuss the disappearance of Dirac cone structure at angles below 1^{\circ}.

13 pages, 17 figures

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• Unconventional Integer Quantum Hall effect in graphene
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Cited by in corpus (257)

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• Twist-controlled resonant tunnelling in graphene-boron nitride-graphene heterostructures
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Colloquium: Graphene spectroscopy
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Band structure and topological property of twisted double bilayer graphenes
• Interlayer coupling in commensurate and incommensurate bilayer structures of transition metal dichalcogenides
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta \sim 1.08^{\circ }$
• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Band structure and insulating states driven by the Coulomb interaction in twisted bilayer graphene
• Interlayer interaction in general incommensurate atomic layers
• The Quantum Twisting Microscope
• Strain-induced quantum phase transitions in magic angle graphene
• Theory of zero-field superconducting diode effect in twisted trilayer graphene
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Flat bands and perfect metal in trilayer moiré graphene
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Magic configurations in Moiré Superlattice of Bilayer Photonic crystal: Almost-Perfect Flatbands and Unconventional Localization
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Optical Conductivity of Twisted Bilayer Graphene
• Highly Tunable Junctions and Nonlocal Josephson Effect in Magic Angle Graphene Tunneling Devices
• Superlattice structures in twisted bilayers of folded graphene
• Electronic Properties of Twisted Trilayer Graphene
• Terahertz conductivity of twisted bilayer graphene
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• Magic-angle Bilayer Phononic Graphene
• Specific Heat of Twisted Bilayer Graphene
• Band structure of twisted bilayer graphene on hexagonal boron nitride
• Heavy fermion representation for twisted bilayer graphene systems
• Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene
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• Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Pair-density-wave and chiral superconductivity in twisted bilayer transition-metal-dichalcogenides
• Bound on resistivity in flat-band materials due to the quantum metric
• Electronic structure of spontaneously strained graphene on hexagonal Boron Nitride
• Spin-twisted Optical Lattices: Tunable Flat Bands and Larkin-Ovchinnikov Superfluids
• Flat bands in magic-angle vibrating plates
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• Electrical switching of a moiré ferroelectric superconductor
• Gate tunable topological flat bands in twisted monolayer-bilayer graphene
• A moiré superlattice on the surface of a topological insulator
• Strain induced quasi-unidimensional channels in twisted moiré lattices
• Electronic localization in twisted bilayer MoS${}_2$ with small rotation angle
• Band-unfolding approach to Moirè-induced band-gap opening and Fermi-level-velocity reduction in twisted bilayer graphene
• Twisted photovoltaics at terahertz frequencies from momentum shift current
• Gate tunable optical absorption and band structure of twisted bilayer graphene
• Observation of Electrically Tunable van Hove Singularities in Twisted Bilayer Graphene from nanoARPES
• Spectral characterization of magic angles in twisted bilayer graphene
• Spin-fluctuation-induced pairing in twisted bilayer graphene
• Impurity-induced triple point fermions in twisted bilayer graphene
• A Combined First Principles Study of the Structural, Magnetic, and Phonon Properties of Monolayer CrI${}_3$
• Moiré magnons in twisted bilayer magnets with collinear order
• TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe${}_2$
• Emergent Localization in Dodecagonal Bilayer Quasicrystals
• Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene
• Twist Angle Tuning of Moiré Exciton Polaritons in van der Waals Heterostructures
• Supermoiré low-energy effective theory of twisted trilayer graphene
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Pressure induced gap modulation and topological transitions in twisted bilayer and double bilayer graphene
• Designing Moiré Patterns by Strain
• Tailoring the band structure of twisted double bilayer graphene with pressure
• Floquet engineering of twisted double bilayer graphene
• The Coexistence of van Hove Singularities and Superlattice Dirac Points in a Slightly Twisted Graphene Bilayer
• Transport across twist angle domains in moiré graphene
• Twistronics in graphene-based van der Waals structures
• Multi-scale lattice relaxation in general twisted trilayer graphenes
• Moiré pattern interlayer potentials in van der Waals materials from random-phase approximation calculations
• Collective excitations and plasmon spectrum in twisted bilayer graphene near the magic angle
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Topological Gaps by Twisting
• Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices
• Topological charge pumping in twisted bilayer graphene
• Recent Developments in Fractional Chern Insulators
• Topological charge pumping by sliding moiré pattern
• Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes
• Bulk valley transport and Berry curvature spreading at the edge of flat bands
• Plasmonic Twistronics: Discovery of Plasmonic Skyrmion Bags
• Single-electron gap in the spectrum of twisted bilayer graphene
• Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Moiré disorder effect in twisted bilayer graphene
• Truncated atomic plane wave method for the subband structure calculations of Moiré systems
• Theoretical methods for excitonic physics in two-dimensional materials
• Topological Sliding Moiré Heterostructure
• Superconductivity induced by the inter-valley Coulomb scattering in a few layers of graphene
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Spin density wave and electron nematicity in magic-angle twisted bilayer graphene
• Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model
• Symmetry breaking in the double moiré superlattices of relaxed twisted bilayer graphene on hexagonal boron nitride
• Valley-selective Floquet Chern Flat Bands in Twisted Multilayer Graphene
• Emergent correlated phases in rhombohedral trilayer graphene induced by proximity spin-orbit and exchange coupling
• Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
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• Fermion sign bounds theory in quantum Monte Carlo simulation
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• From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene
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• Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene
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• Oscillations of van Hove singularities spacing induced by sub-Angstrom fluctuations of interlayer spacing in graphene superlattices
• Vacancy-Engineered Flat-Band Superconductivity in Holey Graphene
• Dynamical properties of quantum many-body systems with long range interactions
• Controllable thermal radiation from twisted bilayer graphen
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• Designing 1D correlated-electron states by non-Euclidean topography of 2D monolayers
• Lattice distortions, moiré phonons, and relaxed electronic band structures in magic-angle twisted bilayer graphene
• Two limit cases of twisted hBN bilayers and their excitonic response
• Graphene on graphene antidot lattices: Electronic and transport properties
• Coupling and decoupling of bilayer graphene monitored by electron energy loss spectroscopy
• Magic angle conditions for twisted 3D topological insulators
• Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
• Full Slonczewski-Weiss-McClure parametrization of few-layer twistronic graphene
• Strange metal behavior of the Hall angle in twisted bilayer graphene
• Enhanced Superconductivity in Quasi-periodic Crystals
• Magic angle twisted bilayer graphene as a highly efficient quantum Otto engine
• Multi-layered atomic relaxation in van der Waals heterostructures
• Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene
• Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition
• Moiré phonons in graphene/hexagonal boron nitride moiré superlattice
• Near-field thermal transport between twisted bilayer graphene
• Metal-Insulator Transition with Charge Fractionalization
• Possible nodeless $s^{\pm }$-wave superconductivity in twisted bilayer graphene
• Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands
• Bose-Einstein condensate-mediated superconductivity in graphene
• Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
• Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition
• Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures
• Magic continuum in twisted bilayer square lattice with staggered flux
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Magnetic skyrmion crystal at a topological insulator surface
• Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer
• Quantum Geometric Exciton Drift Velocity
• Doubled Moiré Flat Bands in Double-twisted Few Layer Graphite
• Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene
• Quantum transport across van der Waals domain walls in bilayer graphene
• Strain-induced conduction gap in vertical devices made of twisted graphene layers
• Vortex Dynamics, Pinning, and Magic Angles on Moiré Patterns
• Effects of heterostrain and lattice relaxation on optical conductivity of twisted bilayer graphene
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Exchange-bias controlled correlations in magnetically encapsulated twisted van der Waals dichalcogenides
• Obstruction and Interference in Low Energy Models for Twisted Bilayer Graphene
• Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
• Time-evolution patterns of electrons in twisted bilayer graphene
• Twisted bilayered graphenes at magic angles and Casimir interactions: correlation-driven effects
• Quasidisorder Induced Topology
• Angle-dependent electron confinement in graphene moiré superlattices
• Effective continuum model of twisted bilayer GeSe and origin of emerging one-dimensional mode
• Twisted bilayer BC${}_3$: Valley interlocked anisotropic flat bands
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• Transparent mirror effect in twist-angle-disordered bilayer graphene
• Topological disorder triggered by interaction-induced flattening of electron spectra in solids
• Theory of intrinsic acoustic plasmons in twisted bilayer graphene
• Spin-orbit correlations and exchange-bias control in twisted Janus dichalcogenide multilayers
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• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
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• Quasiperiodic pairing in graphene quasicrystals
• Approximate symmetries, insulators, and superconductivity in continuum-model description of twisted WSe${}_2$
• Tunable superconductivity and Möbius Fermi surfaces in an inversion-symmetric twisted van der Waals heterostructure
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• Revealing flat bands and hybridization gaps in a twisted bilayer graphene device with microARPES
• General Electronic Structure Calculation Method for Twisted Systems
• A continuum contact model for friction between graphene sheets that accounts for surface anisotropy and curvature
• Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
• Skyrmion Bag Robustness in Plasmonic Bilayer and Trilayer Moiré Superlattices
• Enhanced valley polarization of graphene on hBN under circularly polarized light irradiation
• Moiré excitons in biased twisted bilayer graphene under pressure
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Electronic confinement in quantum dots of twisted bilayer graphene
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Direct observation of moiré flat-band breakdown at the edge of magic-angle twisted bilayer graphene
• Moir{é} pattern assisted geometric resonant tunneling in disordered twisted bilayer graphene
• Neutral magic-angle bilayer graphene: Condon instability and chiral resonances
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Giant chirality-induced spin polarization in twisted transition metal dichalcogenides
• Magic momenta and three dimensional Landau levels from a three dimensional graphite moiré superlattice
• Charge distribution and spin textures in magic-angle twisted bilayer graphene
• Intrinsic and extrinsic photogalvanic effects in twisted bilayer graphene
• Charge and spin correlations in insulating and incoherent metal states of twisted bilayer graphene
• Orbital Frustration and Emergent Flat Bands
• Moiré Band Engineering in Twisted Trilayer WSe2
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Gross-Neveu-XY quantum criticality in moiré Dirac materials
• Short vs. long range exchange interactions in twisted bilayer graphene
• Band manipulation and spin texture in interacting moiré helical edges
• Wigner crystallization at large fine structure constant
• Quantum valley Hall states in low-buckled counterparts of graphene bilayer
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Magnon bands in twisted bilayer honeycomb quantum magnets
• Elastic Screening of Pseudogauge Fields in Graphene
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field
• Magic radius of AA bilayer graphene quantum dot
• Moiré fractals in twisted graphene layers
• Analog of cosmological particle production in Dirac materials
• Origin of magic angles in twisted bilayer graphene: The magic ring
• The low energy excitation spectrum of magic-angle semimetals
• Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene
• Probing the wavefunctions of correlated states in magic angle graphene
• Excitonic Metal and Non-Fermi Liquid Behaviour in Twisted Double Bilayer Graphene near Charge Neutrality
• Coexistence of nematic superconductivity and spin density wave in magic-angle twisted bilayer graphene
• Capturing magic angles in twisted bilayer graphene from information theory markers
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Itinerant topological magnons and spin excitons in twisted transition metal dichalcogenides: Mapping electron topology to spin counterpart
• Stoner ferromagnetism in low-angle twisted bilayer graphene at three-quarters filling
• Artificial gauge fields and topological insulators in Moire superlattices
• Flat-band thermodynamics reveals enhanced performance across Otto, Carnot, and Stirling cycles
• Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Band theory for heterostructures with interface superlattices
• Displacement-field-tunable superconductivity in an inversion-symmetric twisted van der Waals heterostructure
• Experimental evidence of the topological obstruction in twisted bilayer graphene
• Tight binding approximation for bilayer graphene and nanotube structures: from commensurability to incommensurability between the layers
• On dielectric screening in twisted double bilayer graphene
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Twistraintronics in Square Moire Superlattices of Stacked Graphene Layers
• Effective tight-binding models in optical moiré potentials
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene
• Photon absorption in twisted bilayer graphene
• Van der Waals Heterostructure Pt${}_2$HgSe${}_3$/CrI${}_3$ for Topological Valleytronics
• Wavefunction textures in twisted bilayer graphene from first principles
• Collective excitations of the Chern-insulator states in commensurate double moiré superlattices of twisted bilayer graphene on hexagonal boron nitride
• Twisted bilayer graphene from first-principles: structural and electronic properties
• Giant Shear Displacement by Light-Induced Raman Force in Bilayer Graphene
• Low-frequency and Moiré Floquet engineering: a review
• Topological domain-wall states from Umklapp scattering in twisted bilayer graphene
• Flat-band projected versus fully atomistic twisted bilayer graphene
• Interlayer couplings in homobilayer structures of MSi2X4 (M = Mo/W, X = N/P/As)
• Magic distances in twisted bilayer graphene
• Electrodynamics of Thin Sheets of Twisted Material
• The electronic band structures and optical absorption spectra for incommensurate twisted few-layers graphene
• Magnetism of magic-angle twisted bilayer graphene
• Weak localization and universal conductance fluctuations in large area twisted bilayer graphene
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions
• Atomic frustration-based twistronics
• One-dimensional moiré engineering in zigzag graphene nanoribbons on hBN
• The fate of disorder in twisted bilayer graphene near the magic angle
• Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moiré superlattices
• Electrostatic interactions in twisted bilayer graphene
• Moiré-driven equilibrium of perturbations in moiré systems
• Electronic properties of bilayer sheets forming moiré patterns
• Super Moiré Domain Tessellations, Sliding Ferroelectricity, and Reconfigurable Quantum Dot Arrays in Twisted Trilayer Hexagonal Boron Nitride