Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra

Abstract

It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work we disprove this common lore by presenting a theory for all topological ideal flatbands with nonzero Chern number C. The smooth single-particle Bloch wavefunction is proved to admit an exact color-entangled form as a superposition of C lowest Landau level type wavefunctions distinguished by boundary conditions. Including repulsive interactions, Abelian and non-Abelian model fractional Chern insulators of Halperin type are stabilized as exact zero-energy ground states no matter how nonuniform Berry curvature is, as long as the quantum geometry is ideal and the repulsion is short-ranged. The key reason behind is the existence of an emergent Hilbert space in which Berry curvature can be exactly flattened by adjusting wavefunction's normalization. In such space, the flatband-projected density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making exact mapping to C-layered Landau levels possible. In the end we discuss applications of the theory to moire flatband systems with a particular focus on the fractionalized phase and spontaneous symmetry breaking phase recently observed in graphene based twisted materials.

References in corpus (35)

• Graphene Bilayers with a Twist
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Relations between topology and the quantum metric for Chern insulators
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• 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
• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• 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
• 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
• 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
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Nontrivial quantum geometry of degenerate flat bands
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level
• Heuristic bounds on superconductivity and how to exceed them
• Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles
• WKB estimate of bilayer graphene's magic twist angles
• D-Algebra Structure of Topological Insulators
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
• Exact Topological Flat Bands from Continuum Landau Levels

Cited by in corpus (38)

• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Magic-angle helical trilayer graphene
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Ideal Chern bands are Landau levels in curved space
• Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moiré Band of Twisted Bilayer MoTe2
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Higher vortexability: zero field realization of higher Landau levels
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene
• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Intraband collective excitations in fractional Chern insulators are dark
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Bootstrapping the Quantum Hall problem
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Uniqueness of Landau levels and their analogs with higher Chern numbers
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• 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
• Geometric semimetals and their simulation in synthetic matter
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• Three-component fractional quantum Hall effect in topological flat bands
• 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
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Robustness of real-space topology in moiré systems