Commensuration and Interlayer Coherence in Twisted Bilayer Graphene

Abstract

The low energy electronic spectra of rotationally faulted graphene bilayers are studied using a long wavelength theory applicable to general commensurate fault angles. Lattice commensuration requires low energy electronic coherence across a fault and preempts massless Dirac behavior near the neutrality point. Sublattice exchange symmetry distinguishes two families of commensurate faults that have distinct low energy spectra which can be interpreted as energy-renormalized forms of the spectra for the limiting Bernal and AA stacked structures. Sublattice-symmetric faults are generically fully gapped systems due to a pseudospin-orbit coupling appearing in their effective low energy Hamiltonians.

4 pages RevTeX, 3 jpg figures

References in corpus (7)

• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Room-Temperature Superfluidity in Graphene Bilayers
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• The structural properties of the multi-layer graphene/4H-SiC(000-1) system as determined by Surface X-ray Diffraction
• Tunable Graphene System with Two Decoupled Monolayers
• Band structure asymmetry of bilayer graphene revealed by infrared spectroscopy

Cited by in corpus (275)

• Moire bands in twisted double-layer graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• The electronic properties of bilayer graphene
• Graphene Bilayers with a Twist
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Continuum Model of the Twisted Bilayer
• Raman spectroscopy study of rotated double-layer graphene: Misorientation-angle dependence of electronic structure
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Tunable Moiré Bands and Strong Correlations in Small-Twist-Angle Bilayer Graphene
• Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene
• Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
• Optical Absorption in Twisted Bilayer Graphene
• Ultraflat bands and shear solitons in Moiré patterns of twisted bilayer transition metal dichalcogenides
• Electronic properties of graphene-based bilayer systems
• Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS${}_2$
• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
• Numerical studies of confined states in rotated bilayers of graphene
• Electrostatic effects, band distortions and superconductivity in twisted graphene bilayers
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Chiral SDW and d + id superconductivity in the magic-angle twisted bilayer-graphene
• Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
• An exact continuum model for low-energy electronic states of twisted bilayer graphene
• Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
• Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
• Non-Abelian gauge potentials in graphene bilayers
• Moire Butterflies
• Transport Between Twisted Graphene Layers
• Band structure and topological property of twisted double bilayer graphenes
• Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
• Mean-field theory for superconductivity in twisted bilayer graphene
• Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
• 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
• Helical networks in twisted bilayer graphene under interlayer bias
• Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
• Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
• Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene
• Interlayer interaction in general incommensurate atomic layers
• Van Hove Singularities and Excitonic Effects in the Optical Conductivity of Twisted Bilayer Graphene
• Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides
• The Quantum Twisting Microscope
• Band Symmetries and Singularities in Twisted Multilayer Graphene
• Electronic spectrum of twisted bilayer graphene
• Nematic superconductivity in twisted bilayer graphene
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Strong mid-infrared photoresponse in small-twist-angle bilayer graphene
• Proximity effect in graphene-topological insulator heterostructures
• Moiré phonons in the twisted bilayer graphene
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• Electron quantum metamaterials in van der Waals heterostructures
• Continuum model for relaxed twisted bilayer graphenes and moiré electron-phonon interaction
• Optical conductivity, Drude weight and plasmons in twisted graphene bilayers
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Structure of twisted and buckled bilayer graphene
• Breakdown of the interlayer coherence in twisted bilayer graphene
• Novel phases in twisted bilayer graphene at magic angles as a result of van Hove singularities and interactions
• Heterostrain engineering on twisted graphene bilayer around the first magic angle
• Optical Conductivity of Twisted Bilayer Graphene
• Graphene/$\alpha$-RuCl${}_3$: An Emergent 2D Plasmonic Interface
• Quasi-flat plasmonic bands in twisted bilayer graphene
• Disorder in Twisted Bilayer Graphene
• Electronic Properties of Twisted Trilayer Graphene
• A chiral twist on the high-$T_c$ phase diagram in Moiré heterostructures
• Interlayer coupling in rotationally faulted multilayer graphenes
• Local sublattice-symmetry breaking in rotationally faulted multilayer graphene
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Landau Quantization and Fermi Velocity Renormalization in Twisted Graphene Bilayers
• Resonant tunnelling between the chiral Landau states of twisted graphene lattices
• Intrinsically Undamped Plasmon Modes in Narrow Electron Bands
• Derivation of Wannier orbitals and minimal-basis tight-binding hamiltonians for twisted bilayer graphene: a first-principles approach
• Charge redistribution and interlayer coupling in twisted bilayer graphene under electric fields
• Topological carbon materials: a new perspective
• Twists and The Electronic Structure of Graphitic Materials
• Universal phase structure of dilute Bose gases with Rashba spin-orbit coupling
• Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene
• Bilayer Photonic Graphene
• Microscopic correlation between chemical and electronic states in epitaxial graphene on SiC(000-1)
• Phonon mediated interlayer conductance in twisted graphene bilayers
• Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
• Strongly bound excitons dominate electronic relaxation in resonantly excited twisted bilayer graphene
• Angle-Dependent van Hove Singularities and Their Breakdown in Twisted Graphene Bilayers
• Multi-component magneto-optical conductivity of multilayer graphene on SiC
• Magic-angle semimetals
• Twisting Dirac fermions: Circular dichroism in bilayer graphene
• Electron-electron interactions in decoupled graphene layers
• Optical and plasmonic properties of twisted bilayer graphene: Impact of interlayer tunneling asymmetry and ground-state charge inhomogeneity
• Tuning Structures and Electronic Spectra of Graphene Layers by Tilt Grain Boundaries
• Theory of the Raman spectrum of rotated double-layer graphene
• Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene
• Perfect one-dimensional chiral states in biased twisted bilayer graphene
• Flat band in twisted bilayer Bravais lattices
• Direct growth of mm-size twisted bilayer graphene by plasma-enhanced chemical vapor deposition
• Chemical potential asymmetry and quantum oscillations in insulators
• Strain induced quasi-unidimensional channels in twisted moiré lattices
• Twist-angle dependence of electron correlations in moiré graphene bilayers
• Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field
• Band-unfolding approach to Moirè-induced band-gap opening and Fermi-level-velocity reduction in twisted bilayer graphene
• Electronic localization in twisted bilayer MoS${}_2$ with small rotation angle
• Gate tunable optical absorption and band structure of twisted bilayer graphene
• Optical-phonon resonances with saddle-point excitons in twisted-bilayer graphene
• Moiré Band Topology in Twisted Bilayer Graphene
• Multi-carrier Transport in Epitaxial Multi-layer Graphene
• Externally controlled band gap in twisted bilayer graphene
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Mis-orientation controlled cross-plane thermoelectricity in twisted bilayer graphene
• Spectral characterization of magic angles in twisted bilayer graphene
• Magnetic and Kohn-Luttinger instabilities near a Van Hove singularity: monolayer versus twisted bilayer graphene
• Stacking, Strain, & Twist in 2D Materials Quantified by 3D Electron Diffraction
• Isospin and momentum polarized orders in bilayer graphene
• Terahertz photogalvanics in twisted bilayer graphene close to the second magic angle
• Flat-band ferromagnetism in twisted bilayer graphene
• Emergent geometric frustration and flat band in moiré bilayer graphene
• Designing Moiré Patterns by Strain
• Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene
• The Coexistence of van Hove Singularities and Superlattice Dirac Points in a Slightly Twisted Graphene Bilayer
• Twistronics in graphene-based van der Waals structures
• Electron spectrum of epitaxial graphene monolayers
• Time-Reversal Even Charge Hall Effect from Twisted Interface Coupling
• Pairing and non-Fermi liquid behavior in partially flat-band systems
• Topological charge pumping by sliding moiré pattern
• Symmetry of superconducting correlations in displaced bilayers of graphene
• Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system
• Single-electron gap in the spectrum of twisted bilayer graphene
• Marginal Fermi liquid in twisted bilayer graphene
• Topological crystalline insulator phase in graphene multilayers
• Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene
• Electronic properties of asymmetrically doped twisted graphene bilayers
• Truncated atomic plane wave method for the subband structure calculations of Moiré systems
• Stacking transition in bilayer graphene caused by thermally activated rotation
• Theory of Emergent Josephson Lattice in Neutral Twisted Bilayer Graphene (Moiŕe is Different)
• Traits and Characteristics of Interacting Dirac fermions in Monolayer and Bilayer Graphene
• Fermi arc reconstruction at the interface of twisted Weyl semimetals
• New Mechanism for Strongly Bound Excitons in Gapless Two-Dimensional Structures
• Superconductivity in twisted Graphene $\mathrm{NbS}{\mathrm{e}}_2$ heterostructures
• Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems
• Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping
• Moiré edge states in twisted graphene nanoribbons
• Landau Quantization in Twisted Bilayer Graphenes: the Dirac Comb
• AA stacking, tribological and electronic properties of double-layer graphene with krypton spacer
• Topological phases and twisting of graphene on a dichalcogenide monolayer
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Magnon corner states in twisted bilayer honeycomb magnets
• Electronic conductance of twisted bilayer nanoribbon flakes
• Analytical Model for Atomic Relaxation in Twisted Moiré Materials
• A simple derivation of moiré-scale continuous models for twisted bilayer graphene
• Semiclassical Boltzmann transport theory for graphene multilayers
• Quantum Valley Hall effect without Berry curvature
• Orbital magnetic susceptibility of finite-sized graphene
• Duality between atomic configurations and Bloch states in twistronic materials
• Time-reversal versus chiral symmetry breaking in twisted bilayer graphene
• Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers
• Tunable electron-phonon interactions in long-period superlattices
• Unfolding energy spectra of multi-periodicity materials
• Electric Field Tunable Band Gap in Commensurate Twisted Bilayer Graphene
• Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study
• Possible nodeless $s^{\pm }$-wave superconductivity in twisted bilayer graphene
• Origin of layer number dependent linear and nonlinear optical properties of two-dimensional graphene-like SiC
• Piezoelectricity in asymmetrically strained bilayer graphene
• Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures
• Energetic stability and spatial inhomogeneity in the local electronic structure of relaxed twisted trilayer graphene
• High density carriers at a strongly coupled graphene-topological insulator interface
• Generalized Peierls substitution for the tight-binding model of twisted multilayer graphene in a magnetic field
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Magnetic skyrmion crystal at a topological insulator surface
• Electronic structure and quantum transport in twisted bilayer graphene with resonant scatterers
• Quantum transport across van der Waals domain walls in bilayer graphene
• Dirac Magic and Lifshitz Transitions in AA-Stacked Twisted Multilayer Graphene
• Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene
• Terahertz Circular Dichroism in Commensurate Twisted Bilayer Graphene
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Open Momentum Space Method for Hofstadter Butterfly and the Quantized Lorentz Susceptibility
• Twisted Kitaev Bilayers and the Moiré Ising Model
• Nonlinear intensity dependence of photogalvanics and photoconductance induced by terahertz laser radiation in twisted bilayer graphene close to magic angle
• 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
• Twisted bilayer BC${}_3$: Valley interlocked anisotropic flat bands
• Stacking Textures and Singularities in Bilayer Graphene
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• Effective continuum model of twisted bilayer GeSe and origin of emerging one-dimensional mode
• Tunable band gap in twisted bilayer graphene
• Quantum electrodynamics in anisotropic and tilted Dirac photonic lattices
• Theory of intrinsic acoustic plasmons in twisted bilayer graphene
• Crystal Field Effect and Electric Field Screening in Multilayer Graphene with and without Twist
• Quantum Valley and Sub-valley Hall Effect in the Large Angle Twisted Bilayer Graphene
• Approximate symmetries, insulators, and superconductivity in continuum-model description of twisted WSe${}_2$
• A continuum contact model for friction between graphene sheets that accounts for surface anisotropy and curvature
• Strain impacts on commensurate bilayer graphene superlattices: distorted trigonal warping, emergence of bandgap and direct-indirect bandgap transition
• Progress on band structure engineering of twisted bilayer and two-dimensional moiré heterostructures
• Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene
• Transport evidence of superlattice Dirac cones in graphene monolayer on twisted boron nitride substrate
• Enhanced valley polarization of graphene on hBN under circularly polarized light irradiation
• Moiré excitons in biased twisted bilayer graphene under pressure
• Mesoscopic Electronic Transport in Twisted Bilayer Graphene
• Valley splitter and transverse valley focusing in twisted bilayer graphene
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Landau Levels and Band Bending in Few-Layer Epitaxial Graphene
• Transport properties of hybrid single-bilayer graphene interfaces in magnetic field
• An In-situ Annealing effect of Graphene-Graphene Interlayer Conduction
• Lattice dynamics localization in low-angle twisted bilayer graphene
• Giant chirality-induced spin polarization in twisted transition metal dichalcogenides
• Nodal Surfaces in Photoemission from Twisted Bilayer Graphene
• Topological Mixed Valence Model in Magic-Angle Twisted Bilayer Graphene
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
• Comment on "Creating in-plane pseudomagnetic fields in excess of 1000 T by misoriented stacking in a graphene bilayer"
• Absence of Edge States in The Valley Chern Insulator in Moiré Graphene
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• Lattice Deformation, Low Energy Models and Flat Bands in Twisted Graphene Bilayers
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Twisted Bilayer Graphene Superlattices
• Quantum valley Hall states in low-buckled counterparts of graphene bilayer
• Linear and Non-Linear Response of Quadratic Lindbladians
• Emergent flat band lattices in spatially periodic magnetic fields
• Exciton swapping in a twisted graphene bilayer as a solid-state realization of a two-brane model
• Dislocation and node states in bilayer graphene systems
• Moiré-modulated band gap and van Hove singularities in twisted bilayer germanene
• Artificial Relativistic Molecules
• Energy Dispersion, Superconductivity and Magnetic Fluctuations in Stacked Altermagnetism Materials
• Brownian dynamics of Dirac fermions in twisted bilayer graphene
• Moiré fractals in twisted graphene layers
• Chiral Stoner magnetism in Dirac bands
• Effective-mass theory of collapsed carbon nanotubes
• Artificial gauge fields and topological insulators in Moire superlattices
• Ab-initio study of the energy competition between Γand K valleys in bilayer transition metal dichalcogenides
• Stoner ferromagnetism in low-angle twisted bilayer graphene at three-quarters filling
• Twist Angle, Strain, Corrugation and Moire Unit cell in Twisted Bilayer Graphene
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Landau Level Splitting in Rotationally Faulted Multilayer Graphene
• Tuning monolayer superconductivity in twisted NbSe${}_2$ graphene heterostructures
• Tight binding approximation for bilayer graphene and nanotube structures: from commensurability to incommensurability between the layers
• Lattice Model For The Quantum Anomalous Hall Effect in Moiré Graphene
• Spin-charge coupled transport in van der Waals systems with random tunneling
• Signatures of electronic ordering in transport in graphene flat bands
• Exploring interlayer Dirac cone coupling in commensurately rotated few-layer graphene on SiC(000-1)
• Band theory for heterostructures with interface superlattices
• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• Tetrahedral Bonding in Twisted Bilayer Graphene by Carbon Intercalation
• Excitonic effects in twisted bilayer graphene
• Effective theory of rotationally faulted multilayer graphene - the local limit
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• Insulating moiré homobilayers lack a threefold symmetric second harmonic generation
• Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
• Van der Waals Heterostructure Pt${}_2$HgSe${}_3$/CrI${}_3$ for Topological Valleytronics
• Coherent edge mixing and interferometry in quantum Hall bilayers
• Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Twistraintronics in Square Moire Superlattices of Stacked Graphene Layers
• Perpendicular electronic transport and moiré-induced resonance in twisted interfaces of three-dimensional graphite
• Small Angle and Non-Monotonic Behavior of the Thermal Conductivity in Twisted Bilayer Graphene
• Surface Transport and Quantum Hall Effect in Ambipolar Black Phosphorus Double Quantum Wells
• Moiré spintronics: Emergent phenomena, material realization and machine learning accelerating discovery
• Topological domain-wall states from Umklapp scattering in twisted bilayer graphene
• Terahertz Landau level spectroscopy of Dirac fermions in millimeter-scale twisted bilayer graphene
• Anomalous enhancement of large-momentum scattering by electron-electron interaction in moiré superlattices
• Magic distances in twisted bilayer graphene
• The electronic band structures and optical absorption spectra for incommensurate twisted few-layers graphene
• Merged Four Dirac Points at the Critical Interlayer Distance in Commensurately Twisted Bilayer Graphene: the Origin of the Zero Velocity
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Straintronics and twistronics in bilayer graphene
• Weak localization and universal conductance fluctuations in large area twisted bilayer graphene
• Electronic Reconstruction at the Quasicrystal-Moiré Crossover in Twisted Bilayer Graphene
• Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability
• Three-dimensional flat bands and possible interlayer triplet pairing superconductivity in the alternating twisted NbSe${}_2$ moiré bulk
• Atomic frustration-based twistronics
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions
• Magneto-electronic properties of twisted bilayer graphene system
• Electrostatic interactions in twisted bilayer graphene