Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
arXiv:2012.09829 · doi:10.1103/PhysRevB.103.125406
Abstract
We perform an extensive exact diagonalization study of interaction driven insulators in spin- and valley-polarized moiré flat bands of twisted bilayer graphene aligned with its hexagonal boron nitride substrate. In addition to previously reported fractional Chern insulator phases, we provide compelling evidence for competing charge-density-wave phases at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection. The resulting phase diagram features remarkable agreement with experimental findings in a related moiré heterostructure and affirms the relevance of our results beyond the scope of graphene based materials.
arXiv comment16 pages, 18 figures
References in corpus (59)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Moire bands in twisted double-layer graphene
- Tuning superconductivity in twisted bilayer graphene
- Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Graphene bilayer with a twist: electronic structure
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices
- Magic continuum in twisted bilayer WSe2
- Nearly-flat bands with nontrivial topology
- Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
- Abundance of correlated insulating states at fractional fillings of WSe/WS moiré superlattices
- Continuum Model of the Twisted Bilayer
- Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
- Fractional Chern Insulator
- Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
- Untying the insulating and superconducting orders in magic-angle graphene
- Topological Flat Band Models and Fractional Chern Insulators
- Optical Absorption in Twisted Bilayer Graphene
- Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
- Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
- Decoupling superconductivity and correlated insulators in twisted bilayer graphene
- Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe
- Exact results for interacting electrons in high Landau levels
- A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
- Fractional Quantum Hall States and Jack Polynomials
- Observation of fractional Chern insulators in a van der Waals heterostructure
- Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
- Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
- Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
- Geometric and conventional contribution to superfluid weight in twisted bilayer graphene
- Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
- Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: a Hartree-Fock study
- Interlayer interaction in general incommensurate atomic layers
- Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
- Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
- Charge Density Wave Ordering in Half Filled High Landau Levels
- The half-filled Landau level: the case for Dirac composite fermions
- Efficient simulation of moire materials using the density matrix renormalization group
- Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
- Hierarchy of fractional Chern insulators and competing compressible states
- Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene
- Spontaneous Breakdown of Translational Symmetry in Quantum Hall Systems: Crystalline Order in High Landau Levels
- The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
- Wigner Crystals in the lowest Landau level at low filling factors
- Fractional Chern Insulators beyond Laughlin states
- Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
- Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
- A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
- Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
- Pairing in graphene-based moiré superlattices
- Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
- Studying Continuous Symmetry Breaking using Energy Level Spectroscopy
Cited by in corpus (63)
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
- Fractional Chern Insulator in Twisted Bilayer MoTe
- Fractional quantum anomalous Hall states in twisted bilayer MoTe and WSe
- Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
- Topological charge density waves at half-integer filling of a moiré superlattice
- Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
- Topological and stacked flat bands in bilayer graphene with a superlattice potential
- Magic-angle helical trilayer graphene
- Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
- Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
- Quantum geometry in condensed matter
- Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
- Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
- Tunable moiré materials for probing Berry physics and topology
- Quantum Metric Induced Phases in Moiré Materials
- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
- Topological Lattice Models with Constant Berry Curvature
- Phase transitions out of quantum Hall states in moiré materials
- Quantum anomalous Hall crystal at fractional filling of moiré superlattices
- Multiple Chern bands in twisted MoTe and possible non-Abelian states
- Emergence of broken-symmetry states at half-integer band fillings in twisted bilayer graphene
- Recent Developments in Fractional Chern Insulators
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe
- Doping a fractional quantum anomalous Hall insulator
- Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
- Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
- Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
- Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
- Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
- Is attention all you need to solve the correlated electron problem?
- Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
- Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
- Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
- Attractive Haldane bilayers for trapping non-Abelian anyons
- Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
- Quantum anomalous Hall crystals in moiré bands with higher Chern number
- Broken Symmetry in Ideal Chern Bands
- Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
- Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
- Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
- A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
- Parafermions in Moiré Minibands
- Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
- Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
- Identifying Instabilities with Quantum Geometry in Flat Band Systems
- Topological Floquet Flat Bands in Irradiated Alternating Twist Multilayer Graphene
- Adiabatic Continuity of the Spinful Quantum Hall States
- Ordering the topological order in the fractional quantum Hall effect
- Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
- Real-space topology and charge order in the Haldane-Holstein Model
- How quantum fluctuations freeze a classical liquid and then melt it into a topological one
- Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe
- Topological Order Without Band Topology in Moiré Graphene
- Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
- Magnetism of magic-angle twisted bilayer graphene