Fractional quantum Hall effect in the absence of Landau levels

Abstract

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the FQHE in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically nontrivial flat band model on the checkerboard lattice \cite{sun}. In the presence of nearest-neighboring repulsion ($U$), we find that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5 filling, however, a next-nearest-neighboring repulsion is needed for the occurrence of the 1/5 FQHE when $U$ is not too strong. We demonstrate the characteristic features of these novel states and determine the phase diagram correspondingly.

6 pages and 4 figures

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects

Cited by in corpus (270)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• 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
• Correlated Insulating States at Fractional Fillings of the WS2/WSe2 Moiré Lattice
• Genons, twist defects, and projective non-Abelian braiding statistics
• Flat Chern Band in a Two-Dimensional Organometallic Framework
• Exotic electronic states in the world of flat bands: from theory to material
• Correlation effects in two-dimensional topological insulators
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Fractional topological superconductors with fractionalized Majorana fermions
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Flat bands, strange metals, and the Kondo effect
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Flat bands with higher Chern number in pyrochlore slabs
• Observation of novel topological states in hyperbolic lattices
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Exploration and prediction of topological electronic materials based on first-principles calculations
• Bose-Einstein Condensates in Spin-Orbit Coupled Optical Lattices: Flat Bands and Superfluidity
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Polarization-driven band topology evolution in twisted MoTe${}_2$ and WSe${}_2$
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Strongly interacting Majorana fermions
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• 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
• Enhancing the stability of a fractional Chern insulator against competing phases
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Adiabatic continuity between Hofstadter and Chern insulator states
• Topological phases in layered pyrochlore oxide thin films along the [111] direction
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Quantum Metric Induced Phases in Moiré Materials
• Non-Abelian fractionalization in topological minibands
• 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
• Effects of interactions on periodically driven dynamically localized systems
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Desiging Artificial Lieb Lattice on Metal Surface
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Non-Hermitian Mott Skin Effect
• Exceptional band touching for strongly correlated systems in equilibrium
• Continuous Preparation of a Fractional Chern Insulator
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2
• Phase transitions out of quantum Hall states in moiré materials
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Progress and Prospects in Two-Dimensional Magnetism of van der Waals Materials
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Parent Berry curvature and the ideal anomalous Hall crystal
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe${}_2$
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• Observation of the dual quantum spin Hall insulator by density-tuned correlations in a van der Waals monolayer
• Excitonic Condensate in Flat Valence and Conduction Bands of Opposite Chirality
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Damped Dirac magnon in a metallic kagome antiferromagnet FeSn
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Recent Developments in Fractional Chern Insulators
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Orbital Design of Flat Bands in Non-Line-Graph Lattices via Line-Graph Wavefunctions
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Classical Spin Spirals in Frustrated Magnets from Free-Fermion Band Topology
• D-Algebra Structure of Topological Insulators
• Characterization of quasiholes in fractional Chern insulators
• Enhanced fractional quantum Hall gaps in a two-dimensional electron gas coupled to a hovering split-ring resonator
• Composite Fermions on a Torus
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Endless Dirac nodal lines in kagome-metal Ni3In2S2
• Intertwined fractional quantum anomalous Hall states and charge density waves
• Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices
• Emergent flat band and topological Kondo semimetal driven by orbital-selective correlations
• High-order Van Hove singularities and their connection to flat bands
• Two-component quantum Hall effects in topological flat bands
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Interacting bosons in topological optical flux lattices
• Fractional Chern insulators with a non-Landau level continuum limit
• Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Systematic construction of topological flat-band models by molecular-orbital representation
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Fractional Chiral Hinge Insulator
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Interaction driven quantum phase transition in fractional quantum spin Hall effects
• 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${}_2$
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Higher vortexability: zero field realization of higher Landau levels
• Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros
• Fate of exceptional points under interactions: Reduction of topological classifications
• Decoding flat bands from compact localized states
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Doping a fractional quantum anomalous Hall insulator
• Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Fractional quantum anomalous Hall effect in a singular flat band
• SU(N) fractional quantum Hall effects in topological flat bands
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Fractional Chern Insulators in Singular Geometries
• Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Chern Insulators on Singular Geometries
• Elementary formula for the Hall conductivity of interacting systems
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
• Integer and fractional quantum anomalous Hall effects in pentalayer graphene
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Long-lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: a Bosonic Kane-Mele Model Platform
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• \textit{Ab initio} study on spin fluctuations of itinerant kagome magnet FeSn
• ARPES insights on the metallic states of YbB6(001): E(k) dispersion, temporal changes and spatial variation
• Josephson Coupled Moore-Read States
• Correlations and entanglement in flat band models with variable Chern numbers
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
• Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
• Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
• Hyperbolic Fractional Chern insulators
• Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• Interacting phase diagram of twisted bilayer MoTe${}_2$ in magnetic field
• Intraband collective excitations in fractional Chern insulators are dark
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Charge-Neutral Electronic Excitations in Quantum Insulators
• Magnetoresistance and Kondo effect in the nodal-line semimetal VAs${}_2$
• 1D flat bands in phosphorene nanoribbons with pentagonal nature
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Catalogue of Flat-Band Stoichiometric Materials
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Single-particle spectral function of fractional quantum anomalous Hall states
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• Two-dimensional topological order of kinetically constrained quantum particles
• Broken Symmetry in Ideal Chern Bands
• Many-Body Chern Numbers of $\nu =1/3$ and $1/2$ States on Various Lattices
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• On the zero-field quantization of the anomalous quantum Hall effect in moiré 2D layers
• Programmable Hamiltonian engineering with quadratic quantum Fourier transform
• Quantum Monte Carlo simulation of topological phase transitions
• Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator
• Universal Wilson Loop Bound of Quantum Geometry
• Higher-Order Van Hove Singularities in Kagome Topological Bands
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Experimental realization of dice-lattice flat band at the Fermi level in layered electride YCl
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Quantum Hall effects of exciton condensate in topological flat bands
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Fractional quantum Hall effect of Bose-Fermi mixtures
• Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe${}_2$
• Parafermions in Moiré Minibands
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Topologically protected flatness in chiral moiré heterostructures
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Impurity-induced thermal crossover in fractional Chern insulators
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• 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
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Coexisting Kagome and Heavy Fermion Flat Bands in YbCr${}_6$Ge${}_6$
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Static and dynamical magnetic properties of the extended Kitaev-Heisenberg model with spin vacancies
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• Anomalous Bilayer Quantum Hall Effect
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Holographic Lieb lattice and gapping its Dirac band
• Twisted Type-II Rashba Homobilayer: A Platform for Tunable Topological Flat Bands
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Multilayer Haldane model
• Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model
• Variational wavefunctions for fractional topological insulators
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
• Visualizing Electronic Structure of Twisted Bilayer MoTe2 in Devices
• Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy
• Nanoscale Modulation of Flat Bands via Controllable Charge-Density-Waves Defects in 4Hb-TaS2
• Optical signatures of -1/3 fractional quantum anomalous Hall state in twisted MoTe2
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
• Sensing the binding and unbinding of anyons at impurities
• Kerr and Faraday rotations in topological flat and dispersive band structures
• Topological Order in Neural Wavefunctions
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Invisible flat bands on a topological chiral edge
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Orbital Description of Landau Levels
• Reduced Wannier representation for topological bands
• Quantum anomalous Hall domains in a Quenched Topological Mott Insulator
• High-pressure modulation of breathing kagome lattice: Cascade of Lifshitz transitions and evolution of the electronic structure
• Exact Mappings in Condensed Matter Physics
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Gaplessness from disorder and quantum geometry in gapped superconductors
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Robustness of real-space topology in moiré systems
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• General Many-Body Perturbation Framework for Moiré Systems
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective
• Topological Order Without Band Topology in Moiré Graphene
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints
• Stripe antiferromagnetism and chiral superconductivity in tWSe${}_2$
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• Theory of Hofstadter Superconductors
• Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State