Moire Butterflies

Abstract

The Hofstadter butterfly spectral patterns of lattice electrons in an external magnetic field yield some of the most beguiling images in physics. Here we explore the magneto-electronic spectra of systems with moire spatial patterns, concentrating on the case of twisted bilayer graphene. Because long-period spatial patterns are accurately formed at small twist angles, fractal butterfly spectra and associated magneto-transport and magneto-mechanical anomalies emerge at accessible magnetic field strengths.

References in corpus (4)

• Room-Temperature Quantum Hall Effect in Graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Symmetry breaking in commensurate graphene rotational stacking; a comparison of theory and experiment

Cited by in corpus (136)

• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Cloning of Dirac fermions in graphene superlattices
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Graphene Bilayers with a Twist
• Origin of Magic Angles in Twisted Bilayer Graphene
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Tunable Moiré Bands and Strong Correlations in Small-Twist-Angle Bilayer Graphene
• Unravelling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene
• Electronic properties of graphene-based bilayer systems
• Decoupling superconductivity and correlated insulators in twisted bilayer graphene
• Mapping the twist angle and unconventional Landau levels in magic angle graphene
• Phonon scattering dominated electron transport in twisted bilayer graphene
• Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
• Generic Miniband Structure of Graphene on a Hexagonal Substrate
• 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
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
• Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite
• Electronic Structure Theory of Weakly Interacting Bilayers
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Moir{é} patterns as a probe of interplanar interactions: graphene on h-BN
• Interlayer interaction in general incommensurate atomic layers
• Proximity effect in graphene-topological insulator heterostructures
• Magnetic properties of the $\alpha$-$T_3$ model: magneto-optical conductivity and the Hofstadter butterfly
• Structure of twisted and buckled bilayer graphene
• The Landau Level of Fragile Topology
• Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene
• Superlattice structures in twisted bilayers of folded graphene
• Interlayer coupling in rotationally faulted multilayer graphenes
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Moire superlattice effects in graphene/boron-nitride van der Waals heterostructures
• Landau levels in twisted bilayer graphene and semiclassical orbits
• Magic-angle Bilayer Phononic Graphene
• Topological carbon materials: a new perspective
• Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking
• Heavy fermion representation for twisted bilayer graphene systems
• Bilayer Photonic Graphene
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
• Optical absorption of twisted bilayer graphene with interlayer potential asymmetry
• Dirac edges of fractal magnetic minibands in graphene with hexagonal moire superlattices
• Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field
• Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25T ($2\pi$ Flux)
• Gate tunable optical absorption and band structure of twisted bilayer graphene
• Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly
• Spectral characterization of magic angles in twisted bilayer graphene
• Supermoiré low-energy effective theory of twisted trilayer graphene
• Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Topological Valley Currents in Bilayer Graphene/Hexagonal Boron Nitride Superlattices
• Optical properties of the Hofstadter butterfly in the Moiré superlattice
• Transport and particle-hole asymmetry in graphene on boron nitride
• Moiré minibands in graphene heterostructures with almost commensurate sqrt3 x sqrt3 hexagonal crystals
• Generation and morphing of plasmons in graphene superlattices
• Gap Structure of the Hofstadter System of Interacting Dirac Fermions in Graphene
• Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene
• Electronic properties of asymmetrically doped twisted graphene bilayers
• Unusual magnetotransport in twisted bilayer graphene
• Revealing Hofstadter Spectrum for Graphene in a Periodic Potential
• Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux
• Symmetries as the guiding principle for flattening bands of Dirac fermions
• Landau Quantization in Twisted Bilayer Graphenes: the Dirac Comb
• Emergence of Chern insulating states in non-Magic angle twisted bilayer graphene
• Voltage-controlled long-range propagation of indirect excitons in van der Waals heterostructure
• A simple derivation of moiré-scale continuous models for twisted bilayer graphene
• Narrow bands in magnetic field and strong-coupling Hofstadter spectra
• Resonant tunneling and the quasiparticle lifetime in graphene/boron nitride/graphene heterostructures
• Quantum Spin Hall Effect in Twisted Bilayer Graphene
• Topologically Universal Spectral Hierarchies of Quasiperiodic Systems
• Magic angle twisted bilayer graphene as a highly efficient quantum Otto engine
• Moiré Landau fans and magic zeros
• Magnetic Breakdown in Twisted Bilayer Graphene
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum
• Spectroscopy of the Fractal Hofstadter Energy Spectrum
• Dynamic polarization and plasmons in kekulé-patterned graphene: Signatures of the broken valley degeneracy
• Piezoelectricity in asymmetrically strained bilayer graphene
• Magic continuum in twisted bilayer square lattice with staggered flux
• Magnetic field stabilized Wigner crystal states in a graphene moiré superlattice
• Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride
• High density carriers at a strongly coupled graphene-topological insulator interface
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Open Momentum Space Method for Hofstadter Butterfly and the Quantized Lorentz Susceptibility
• Optical imprinting of superlattices in two-dimensional materials
• Angle-dependent electron confinement in graphene moiré superlattices
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Topological heavy fermions in magnetic field
• Replica Higher-Order Topology of Hofstadter Butterflies in Twisted Bilayer Graphene
• Nematic insulator at charge neutrality in twisted bilayer graphene
• Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN
• In-plane Chiral Tunneling and Out-of-plane Valley-polarized Quantum Tunneling in Twisted Graphene Trilayer
• Transport evidence of superlattice Dirac cones in graphene monolayer on twisted boron nitride substrate
• THz conductivity of graphene on boron nitride
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• An In-situ Annealing effect of Graphene-Graphene Interlayer Conduction
• Magic momenta and three dimensional Landau levels from a three dimensional graphite moiré superlattice
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Moiré Band Engineering in Twisted Trilayer WSe2
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field
• Stable $2R$ van der Waals heterostructures of NbS${}_2$ and $M$Se${}_2$ for $M$=Mo and W
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Probing Layer Localization in Twisted Graphene Bilayers via Cyclotron Resonance
• Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials
• Realization and transport investigation of a single layer-twisted bilayer graphene junction
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Effective-mass theory of collapsed carbon nanotubes
• Hofstadter butterflies in magnetically modulated graphene bilayer: an algebraic approach
• Exceptional topology in non-Hermitian twisted bilayer graphene
• Excitonic effects in twisted bilayer graphene
• Direct observation of locally modified excitonic effect within a moiré unit cell in twisted bilayer graphene
• Fractal non-Fermi liquids from moiré-Hofstadter phonons
• Emergent Symmetry and Valley Chern Insulator in Twisted Double-Bilayer Graphene
• Flat-band thermodynamics reveals enhanced performance across Otto, Carnot, and Stirling cycles
• Excitation Gap of Fractal Quantum Hall States in Graphene
• Hofstadter-Moiré Butterfly in Twisted Trilayer Graphene
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Magnetic Hofstadter cascade in a twisted semiconductor homobilayer
• Coherent edge mixing and interferometry in quantum Hall bilayers
• Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene
• Photon absorption in twisted bilayer graphene
• Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential
• The electronic band structures and optical absorption spectra for incommensurate twisted few-layers graphene
• Hexagonal boron nitride/bilayer graphene moiré superlattices in the Dirac-material family: energy-band engineering and carrier doping by dual gating
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields
• Trigonal Quasicrystalline States in $30^{\circ }$ Rotated Double Moiré Superlattices
• Hofstadter Butterfly in Graphene
• One-dimensional moiré engineering in zigzag graphene nanoribbons on hBN
• Floquet Control of Electron and Exciton Transport in Kekulé-Distorted Graphene