Fractional Chern Insulator

Abstract

Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall effect and rule out charge-density wave states that have not been ruled out by previous studies. By diagonalizing the Hubbard interaction in the flat-band limit of these insulators, we show the following: The system is incompressible and has a 3-fold degenerate ground state whose momenta can be computed by postulating an generalized Pauli principle with no more than 1 particle in 3 consecutive orbitals. The ground state density is constant, and equal to 1/3 in momentum space. Excitations of the system are fractional statistics particles whose total counting matches that of quasiholes in the Laughlin state based on the same generalized Pauli principle. The entanglement spectrum of the state has a clear entanglement gap which seems to remain finite in the thermodynamic limit. The levels below the gap exhibit counting identical to that of Laughlin 1/3 quasiholes. Both the 3 ground states and excited states exhibit spectral flow upon flux insertion. All the properties above disappear in the trivial state of the insulator - both the many-body energy gap and the entanglement gap close at the phase transition when the single-particle Hamiltonian goes from topologically nontrivial to topologically trivial. These facts clearly show that fractional many-body states are possible in topological insulators.

13 pages, 16 figures

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Cited by in corpus (468)

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• Bosonic integer quantum Hall states in topological bands with Chern number two
• Stability of fractional Chern insulators with a non-Landau level continuum limit
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• Crystal-symmetry preserving Wannier states for fractional chern insulators
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• Intercomponent entanglement entropy and spectrum in binary Bose-Einstein condensates
• Dynamic mass generation and topological order in overscreened Kondo lattices
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Higher-Order Van Hove Singularities in Kagome Topological Bands
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• Exact Topological Flat Bands from Continuum Landau Levels
• Universal Wilson Loop Bound of Quantum Geometry
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• Bounds for low-energy spectral properties of center-of-mass conserving positive two-body interactions
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• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Fractional quantum Hall effect of Bose-Fermi mixtures
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Entanglement in 3D Kitaev Spin Liquids
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
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• Dynamical Signatures of Liouvillian Flat Band
• 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
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Hierarchy of correlations: Application to Green's functions and interacting topological phases
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• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
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• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
• Impurity-induced thermal crossover in fractional Chern insulators
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Frustrated quantum spin systems in small triangular lattices studied with a numerical method
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Superlattice induced electron percolation within a single Landau level
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Anomalous Bilayer Quantum Hall Effect
• Hofstadter-Moiré Butterfly in Twisted Trilayer Graphene
• Continuum limit of lattice quasielectron wavefunctions
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Crystalline invariants of fractional Chern insulators
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Reordering Fractional Chern Insulators into Stripes of Fractional Charges with Long-Range Interactions
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Variational wavefunctions for fractional topological insulators
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Candidate for a Fractional Topological Insulator in Twisted MoTe2
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Numerical identification and gapped boundaries of abelian fermionic topological order
• Tunable Flux Vortices in 2D Dirac Superconductors
• Few-particle dynamics of fractional quantum Hall lattice models
• Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model
• Homogeneous Magnetic Flux in Rydberg Lattices
• Visualizing Electronic Structure of Twisted Bilayer MoTe2 in Devices
• Twisted Type-II Rashba Homobilayer: A Platform for Tunable Topological Flat Bands
• On the geometrical description of fractional Chern insulators based on static structure factor calculations
• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• Sensing the binding and unbinding of anyons at impurities
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Topological Order in Neural Wavefunctions
• Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
• Optical signatures of -1/3 fractional quantum anomalous Hall state in twisted MoTe2
• Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene
• Chiral spin liquid from magnetic Wannier states
• Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators
• Non-Abelian line graph: A generalized approach to flat bands
• Correlation-driven non-trivial phases in single bi-layer Kagome intermetallics
• Dynamics of quasiholes and quasiparticles at the edges of small lattices
• Volkov-Pankratov states on the edge of a quantum spin Hall system
• Stripe antiferromagnetism and chiral superconductivity in tWSe${}_2$
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Flux attachment theory of fractional excitonic insulators
• Topological Order Without Band Topology in Moiré Graphene
• Gaplessness from disorder and quantum geometry in gapped superconductors
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• High-pressure modulation of breathing kagome lattice: Cascade of Lifshitz transitions and evolution of the electronic structure
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model
• Bloch classification surface for three-band systems
• Defect-induced edge ferromagnetism and fractional spin excitations of the SU(4) $\pi$-flux Hubbard model on honeycomb lattice
• Distinct topological excitonic insulators characterized by quantum geometry
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Theory of Hofstadter Superconductors
• Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives
• Orbital Description of Landau Levels
• Insulating charge transfer ferromagnetism
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• General Many-Body Perturbation Framework for Moiré Systems
• Evolution of the optimal trial wave function with interactions in fractional Chern insulators
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Invisible flat bands on a topological chiral edge
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$
• Robustness of real-space topology in moiré systems
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Ferromagnetic--nematic order and strongly correlated phases of fermions in optical flux lattices
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints