Fractional Chern Insulators beyond Laughlin states

Abstract

We report the first numerical observation of composite fermion (CF) states in fractional Chern insulators (FCI) using exact diagonalization. The ruby lattice Chern insulator model for both fermions and bosons exhibits a clear signature of CF states at filling factors 2/5 and 3/7 (2/3 and 3/4 for bosons). The topological properties of these states are studied through several approaches. Quasihole and quasielectron excitations in FCI display similar features as their fractional quantum hall (FQH) counterparts. The entanglement spectrum of FCI groundstates shows an identical fingerprint to its FQH partner. We show that the correspondence between FCI and FQH obeys the emergent symmetry already established, proving the validity of this approach beyond the clustered states. We investigate other Chern insulator models and find similar signatures of CF states. However, some of these systems exhibit strong finite size effects.

9 pages with supplementary material, 13 figures, published version

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• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
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• Bosonic Mott Insulator with Meissner Currents
• Hierarchy of fractional Chern insulators and competing compressible states
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• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
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• Quantum Metric Induced Phases in Moiré Materials
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Bulk-edge correspondence in fractional Chern insulators
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Characterization of quasiholes in fractional Chern insulators
• Wigner crystallization in topological flat bands
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Chern-Simons Composite Fermion Theory of Fractional Chern Insulators
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Edge Excitations in Fractional Chern Insulators
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Exotic Fractional Topological States in Two-Dimensional Organometallic Material
• Fractional Quantum Hall States of Dipolar Gases in Chern Bands
• Realizing Topological Mott Insulators from the RKKY Interaction
• Growing quantum states with topological order
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• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Reordering Fractional Chern Insulators into Stripes of Fractional Charges with Long-Range Interactions
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Exact Mappings in Condensed Matter Physics
• Family of High-Chern-Number Orbital Magnets in Twisted Rhombohedral Graphene
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints