Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers

Abstract

Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number $C$ with ideal quantum geometry. While $C>1$ bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number $1$ that are intertwined through translation and rotation symmetry. The decomposed bands admit an $SU(C)$ action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the $SU(C)$ action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

14+10 pages, 8 figures

References in corpus (64)

• Fractional quantum Hall states at zero magnetic field
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Untying the insulating and superconducting orders in magic-angle graphene
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
• Electrical switching of magnetic order in an orbital Chern insulator
• Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
• Tunable correlation-driven symmetry breaking in twisted double bilayer graphene
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Flatbands in twisted double bilayer graphene
• Topological flat band models with arbitrary Chern numbers
• Electronic phase separation in topological surface states of rhombohedral graphite
• Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Relations between topology and the quantum metric for Chern insulators
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• 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
• Multiple-Q Instability by (d-2)-dimensional Connections of Fermi Surfaces
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Topological charge density waves at half-integer filling of a moiré superlattice
• Universal moiré nematic phase in twisted graphitic systems
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Tunable quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene
• Electronic Properties of Twisted Trilayer Graphene
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene
• Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• 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
• Visualizing delocalized correlated electronic states in twisted double bilayer graphene
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Topological Lattice Models with Constant Berry Curvature
• Spectral characterization of magic angles in twisted bilayer graphene
• Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene
• Imaging topological torus lattice from an electron crystal in twisted mono-bilayer graphene
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles
• Recent Developments in Fractional Chern Insulators
• WKB estimate of bilayer graphene's magic twist angles
• Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems
• Spectroscopic visualization of flat bands in magic-angle twisted monolayer-bilayer graphene: localization-delocalization coexisting electronic states
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Fractional Chern insulators with a non-Landau level continuum limit
• Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
• Revealing Chern number from quantum metric
• Moire Band Structures of the Double twisted Few Layer Graphene
• Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking
• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
• Phase diagram and orbital Chern insulator in twisted double bilayer graphene
• Moiré Flat Bands of Twisted Few-layer Graphite

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• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
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• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
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• Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
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• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
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• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Many-Body Quantum Geometric Dipole
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Designing (higher) Hall crystals
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• Three-component fractional quantum Hall effect in topological flat bands
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Robustness of real-space topology in moiré systems
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory