Nearly Flat Chern Bands in Moiré Superlattices

Abstract

Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moiré super-lattice is formed. Each layer is chosen to be either AB stacked bilayer graphene (BG), ABC stacked trilayer graphene (TG), or hexagonal boron nitride (h-BN). In these systems a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be $\pm 0,\pm 1,\pm 2,\pm 3$ depending on the specific system and vertical electrical field. We show that these graphene moiré super-lattices are promising platforms to realize a number of fascinating many-body phenomena, including (Fractional) Quantum Anomalous Hall Effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.

24 pages+9 figures; version 2: changed language

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Cited by in corpus (276)

• Tuning superconductivity in twisted bilayer graphene
• Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Origin of Magic Angles in Twisted Bilayer Graphene
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Electric Field Tunable Correlated States and Magnetic Phase Transitions in Twisted Bilayer-Bilayer Graphene
• Signatures of Gate-Tunable Superconductivity in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
• Correlated states in twisted double bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Colloquium: Quantum anomalous Hall effect
• Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
• Twisted Bilayer Graphene: A Phonon Driven Superconductor
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Half and quarter metals in rhombohedral trilayer graphene
• Electrical switching of magnetic order in an orbital Chern insulator
• Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
• Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Magic Angle Hierarchy in Twisted Graphene Multilayers
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Designing Flat Band by Strain
• Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene
• Flatbands in twisted double bilayer graphene
• Imaging orbital ferromagnetism in a moiré Chern insulator
• Twisted bilayer graphene III. Interacting Hamiltonian and exact symmetries
• Ferromagnetism in narrow bands of moiré superlattices
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Berry curvature dipole senses topological transition in a moiré superlattice
• Twisted Bilayer Graphene V: Exact Analytic Many-Body Excitations in Twisted Bilayer Graphene Coulomb Hamiltonians: Charge Gap, Goldstone Modes and Absence of Cooper Pairing
• Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
• Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene
• Moiré Flat Bands in Twisted Double Bilayer Graphene
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
• Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Giant Orbital Magneto-electric effect and Current-driven Magnetization Switching in Twisted Bilayer Graphene
• In situ twistronics of van der Waals heterostructures
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Quantum Anomalous Hall Effect in Antiferromagnetism
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Coexistence of ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched trilayer 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
• Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Topological charge density waves at half-integer filling of a moiré superlattice
• Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• The Landau Level of Fragile Topology
• Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe${}_2$/WSe${}_2$ Heterobilayers
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Symmetry breaking and skyrmionic transport in twisted bilayer graphene
• Moiré Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride
• A chiral twist on the high-$T_c$ phase diagram in Moiré heterostructures
• Magic-angle helical trilayer graphene
• Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice
• Charge Smoothening and Band Flattening due to Hartree corrections in Twisted Bilayer Graphene
• Topological flat bands in twisted trilayer graphene
• Flat Chern Band From Twisted Bilayer MnBi${}_2$Te${}_4$
• Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene
• Spectroscopy Signatures of Electron Correlations in a Trilayer Graphene/hBN Moiré Superlattice
• Anomalous Hall effect at half filling in twisted bilayer graphene
• Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene
• Tunable large Berry dipole in strained twisted bilayer graphene
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Twists and The Electronic Structure of Graphitic Materials
• Intrinsic Band Gap and Electrically Tunable Flat Bands in Twisted Double Bilayer Graphene
• Giant nonlinear Hall effect in strained twisted bilayer graphene
• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
• Topological Phases in AB-Stacked MoTe${}_2$/WSe${}_2$: ${\mathbb{Z}}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• Optically induced flat bands in twisted bilayer graphene
• Valley Jahn-Teller effect in twisted bilayer graphene
• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
• Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
• Superconductivity in Twisted Double Bilayer Graphene Stabilized by WSe${}_2$
• Tunable moiré materials for probing Berry physics and topology
• Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
• Anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted graphene systems
• Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene
• Band flattening in buckled monolayer graphene
• Quantum Metric Induced Phases in Moiré Materials
• Gate tunable topological flat bands in twisted monolayer-bilayer graphene
• Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene
• Pseudo-magnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamitonians of twisted bilayer graphene
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Pairing symmetry of twisted bilayer graphene: a phenomenological synthesis
• Ferromagnetism and superconductivity in twisted double bilayer graphene
• Spin-valley density wave in moiré materials
• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Spectroscopy of a Tunable Moiré System with a Correlated and Topological Flat Band
• Pairing in graphene-based moiré superlattices
• Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories
• Phase transitions out of quantum Hall states in moiré materials
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Tunable bandwidths and gaps in twisted double bilayer graphene system on the verge of correlations
• Parent Berry curvature and the ideal anomalous Hall crystal
• Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
• Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization
• Flat-band ferromagnetism in twisted bilayer graphene
• Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene
• Tailoring the band structure of twisted double bilayer graphene with pressure
• Floquet engineering of twisted double bilayer graphene
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Quasiperiodicity, band topology, and moiré graphene
• Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Nonlinear Hall Effects in Strained Twisted Bilayer WSe${}_2$
• Twistronics in graphene-based van der Waals structures
• Tunable ferromagnetism at non-integer filling of a moiré superlattice
• Electrical control of spin and valley in spin-orbit coupled graphene multilayers
• Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices
• Twisted bilayer graphene in a parallel magnetic field
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• Recent Developments in Fractional Chern Insulators
• Intrinsic spin Hall torque in a moire Chern magnet
• Bulk valley transport and Berry curvature spreading at the edge of flat bands
• Correlated Insulating Phases in the Twisted Bilayer Graphene
• Doping-induced quantum spin Hall insulator to superconductor transition
• Electron spin resonance and collective excitations in magic-angle twisted bilayer graphene
• Lattice relaxation, mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene
• Symmetry of superconducting correlations in displaced bilayers of graphene
• Marginal Fermi liquid in twisted bilayer graphene
• Degradation of phonons in disordered moiré superlattices
• Electron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Ferromagnetism and Spin-Valley liquid states in Moiré Correlated Insulators
• Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator
• Topological Sliding Moiré Heterostructure
• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Current-induced reversal of anomalous Hall conductance in twisted bilayer graphene
• Phonon scattering induced carrier resistivity in twisted double bilayer graphene
• Mott insulating state and $d+id$ superconductivity in an ABC graphene trilayer
• Emergent magnetic texture in driven twisted bilayer graphene
• Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
• Excitonic Chern insulator and kinetic ferromagnetism in MoTe${}_2$/WSe${}_2$ moiré bilayer
• Valley-selective Floquet Chern Flat Bands in Twisted Multilayer Graphene
• SU(4) symmetry in twisted bilayer graphene - an itinerant perspective
• Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• DMRG study of strongly interacting ${\mathbb{Z}}_2$ flatbands: a toy model inspired by twisted bilayer graphene
• Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene
• Multilayer graphene with a superlattice potential
• Emergence of Chern insulating states in non-Magic angle twisted bilayer graphene
• ${\phi }_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state
• Current Driven Magnetization Reversal in Orbital Chern Insulators
• Topological flat bands without magic angles in massive twisted bilayer graphenes
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
• Chern Number Tunable Quantum Anomalous Hall Effect in Compensated Antiferromagnets
• Strain-induced large injection current in twisted bilayer graphene
• Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field
• From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene
• Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene
• Symmetry constraints on superconductivity in twisted bilayer graphene: Fractional vortices, $4e$ condensates or non-unitary pairing
• Moire Band Structures of the Double twisted Few Layer Graphene
• Doping a fractional quantum anomalous Hall insulator
• Current Switching of Valley Polarization in Twisted Bilayer Graphene
• Strong correlations in ABC-stacked trilayer graphene: Moiré is important
• Time-reversal versus chiral symmetry breaking in twisted bilayer graphene
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• Quantum anomalous Hall effect and electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moiré heterobilayers
• Trions in Twisted Bilayer Graphene
• Electronic Raman Scattering in Twistronic Few-Layer Graphene
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Metal-Insulator Transition with Charge Fractionalization
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Topological Flat Bands in Graphene Super-moiré Lattices
• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
• Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition
• Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene
• Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands
• Magnetic phases from competing Hubbard and extended Coulomb interactions in twisted bilayer graphene
• Magnetic field stabilized Wigner crystal states in a graphene moiré superlattice
• Quantum Hall spin liquids and their possible realization in moiré systems
• Twisted-bilayer FeSe and the Fe-based superlattices
• Theory of plasmonic edge states in chiral bilayer systems
• Doubled Moiré Flat Bands in Double-twisted Few Layer Graphite
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Moiré Flat Bands of Twisted Few-layer Graphite
• Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS${}_2$
• Josephson effect in graphene bilayers with adjustable relative displacement
• Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
• Topological phases in N-layer ABC-graphene boron-nitride moire superlattices
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Superconductivity in twisted multilayer graphene: a smoking gun in recent condensed matter physics
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene
• Double and Quadruple Flat Bands tuned by Alternative magnetic Fluxes in Twisted Bilayer Graphene
• Quantum Geometric Oscillations in Two-Dimensional Flat-Band Solids
• On the nature of the correlated insulator states in twisted bilayer graphene
• Theory of ARPES in Graphene-Based Moiré Superlattices
• Chern-insulator phases and spontaneous spin and valley order in a moiré lattice model for magic-angle twisted bilayer graphene
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Tunable quantum interferometer for correlated moiré electrons
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Textured Exciton Insulators
• Electric-field switchable chirality in rhombohedral graphene Chern insulators stabilized by tungsten diselenide
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Absence of Edge States in The Valley Chern Insulator in Moiré Graphene
• LAN -- A materials notation for 2D layered assemblies
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Orbital Frustration and Emergent Flat Bands
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Topological $p_x+i{p}_y$ inter-valley coherent state in Moiré MoTe${}_2$/WSe${}_2$ heterobilayers
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Quantum geometric moment encodes stacking order of moiré matter
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Quantum Hall effects of exciton condensate in topological flat bands
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field
• Evolution between quantum Hall and conducting phases: simple models and some results
• Emergence of intrinsically isolated flat bands and their topology in fully relaxed twisted multi-layer graphene
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
• Anomalous continuous symmetries and quantum topology of Goldstone modes
• Parafermions in Moiré Minibands
• Spontaneous symmetry breaking in a honeycomb lattice subject to a periodic potential
• Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Momentum-space theory for topological magnons in 2D ferromagnetic skyrmion lattices
• Weak localization on moiré superlattice in twisted double bilayer graphene
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Floquet Hofstadter butterfly in trilayer graphene with a twisted top layer
• Emergent Symmetry and Valley Chern Insulator in Twisted Double-Bilayer Graphene
• On dielectric screening in twisted double bilayer graphene
• Emergent topology of flat bands in a twisted bilayer $\alpha$-$T_3$ lattice
• Topological Floquet Flat Bands in Irradiated Alternating Twist Multilayer Graphene
• Lattice Model For The Quantum Anomalous Hall Effect in Moiré Graphene
• Anomalous Bilayer Quantum Hall Effect
• Topological phase transition from periodic edge states in moiré superlattices
• Layer-Resolved Quantum Transport in Twisted Bilayer Graphene: Counterflow and Machine Learning Predictions
• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
• Ordering the topological order in the fractional quantum Hall effect
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
• Energy Spectrum Theory of Incommensurate Systems
• Magnetic ordering tendencies in hexagonal boron nitride-bilayer graphene moiré structures
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Decomposing Electronic Structures in Twisted Multilayers: Bridging Spectra and Incommensurate Wave Functions
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
• Particle-hole asymmetric phases in doped twisted bilayer graphene
• Prediction of the Hubbard U parameter from scanning tunneling microscopy images of moire systems using image recognition