Topological Flat Band Models and Fractional Chern Insulators

Abstract

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with non-zero Chern number, $C$. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with non-trivial topology, $C\ne 0$, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with $|C|>1$. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.

Invited review. 46 pages, many illustrations and references. V2: final version with minor improvements and added references

References in corpus (106)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Maximally localized Wannier functions: Theory and applications
• Area laws for the entanglement entropy - a review
• Topological entanglement entropy
• Quantum Spin Hall Effect
• Detecting topological order in a ground state wave function
• Artificial gauge potentials for neutral atoms
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Cloning of Dirac fermions in graphene superlattices
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Identifying Topological Order by Entanglement Entropy
• Fractional quantum Hall states of atoms in optical Lattices
• Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures
• Wannier representation of Z_2 topological insulators
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Geometrical Description of the Fractional Quantum Hall Effect
• Fractional Quantum Hall States and Jack Polynomials
• Fractional topological insulators
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Nearly flat band with Chern number C=2 on the dice lattice
• PEPS as ground states: degeneracy and topology
• Flat Chern Band in a Two-Dimensional Organometallic Framework
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Characterizing topological order by studying the ground states of an infinite cylinder
• Correlation effects in two-dimensional topological insulators
• Realizing Fractional Chern Insulators with Dipolar Spins
• Electron interactions in graphene in a strong magnetic field
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Zoology of Fractional Chern Insulators
• Topological flat band models with arbitrary Chern numbers
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Fractional topological insulators in three dimensions
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Fractional Chern Insulators and the W-Infinity Algebra
• High field fractional quantum Hall effect in optical lattices
• Extracting Excitations From Model State Entanglement
• Correlated Topological Insulators and the Fractional Magnetoelectric Effect
• Quantum Hall system in Tao-Thouless limit
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Exact Matrix Product States for Quantum Hall Wave Functions
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• How to Measure the Quantum Geometry of Bloch Bands
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• Topological Flat Bands from Dipolar Spin Systems
• Fractional topological phases and broken time reversal symmetry in strained graphene
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Matrix Product States for Trial Quantum Hall States
• Enhancing the stability of a fractional Chern insulator against competing phases
• Pseudopotential Formalism for Fractional Chern Insulators
• Fractional Chern Insulators beyond Laughlin states
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Time-reversal symmetric hierarchy of fractional incompressible liquids
• Adiabatic continuity between Hofstadter and Chern insulator states
• From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect
• Topological phases in layered pyrochlore oxide thin films along the [111] direction
• Epitaxial growth of (111)-oriented LaAlO${}_3$/LaNiO${}_3$ ultra-thin superlattices
• Topology-induced phase transitions in quantum spin Hall lattices
• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
• Flat bands with non-trivial topology in three dimensions
• Hamiltonian theory of fractionally filled Chern bands
• Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons
• Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
• Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Fractional Chern Insulators from the nth Root of Bandstructure
• Designing Topological Bands in Reciprocal Space
• Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands
• Narrowing of topological bands due to electronic orbital degrees of freedom
• Unraveling of the fractional topological phase in one-dimensional flatbands with nontrivial topology
• Orthogonal localized wave functions of an electron in a magnetic field
• S-duality constraints on 1D patterns associated with fractional quantum Hall states
• Establishing non-Abelian topological order in Gutzwiller projected Chern insulators via Entanglement Entropy and Modular S-matrix
• Bulk-edge correspondence in fractional Chern insulators
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Momentum-space instantons and maximally localized flat-band topological Hamiltonians
• Elementary formula for the Hall conductivity of interacting systems
• Topological Phenomena in Trapped Ion Systems
• Viewpoint: Toward Fractional Quantum Hall physics with cold atoms

Cited by in corpus (345)

• Classification of topological quantum matter with symmetries
• Atomic quantum gases in periodically driven optical lattices
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Artificial flat band systems: from lattice models to experiments
• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Nearly Flat Chern Bands in Moiré Superlattices
• Interacting topological insulators: a review
• Novel effects of strains in graphene and other two dimensional materials
• Geometric origin of superfluidity in the Lieb lattice flat band
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Band geometry, Berry curvature and superfluid weight
• Floquet Fractional Chern Insulator in Doped Graphene
• Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Quantum Hall Physics - hierarchies and CFT techniques
• Exotic electronic states in the world of flat bands: from theory to material
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Detangling Flat Bands into Fano Lattices
• Classification of flat bands according to the band-crossing singularity of Bloch wave functions
• Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling
• Particle-Hole Duality, Emergent Fermi Liquids and Fractional Chern Insulators in Moiré Flatbands
• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Flat Bands Under Correlated Perturbations
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Non-Bloch band collapse and chiral Zener tunneling
• Unconventional Flatband Line States in Photonic Lieb Lattices
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Periodically-driven quantum matter: the case of resonant modulations
• Quantum metric and effective mass of a two-body bound state in a flat band
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Flat band states: disorder and nonlinearity
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Geometric stability of topological lattice phases
• Landau-Zener Bloch oscillations with perturbed flat bands
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Fractionalized Topological Insulators
• 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
• Band structure engineering of ideal fractional Chern insulators
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe${}_2$/WSe${}_2$ Heterobilayers
• First-Principles Design of a Half-Filled Flat Band of the Kagome Lattice in Two-Dimensional Metal-Organic Frameworks
• Non-Hermitian fractional quantum Hall states
• Chiral Topological Phases from Artificial Neural Networks
• Flat bands in lattices with non-Hermitian coupling
• Realization of a density-dependent Peierls phase in a synthetic, spin-orbit coupled Rydberg system
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Phases of correlated spinless fermions on the honeycomb lattice
• Topological flat bands in twisted trilayer graphene
• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• Topological Creutz Ladder in a Resonantly Shaken 1D Optical Lattice
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Disordered flat bands on the kagome lattice
• Engineering topological materials in microwave cavity arrays
• Fractional (Chern and topological) insulators
• 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
• Quantum geometry in condensed matter
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Scattering matrix invariants of Floquet topological insulators
• Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films
• Dynamic optical lattices of sub-wavelength spacing for ultracold atoms
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Flat-band localization in Creutz superradiance lattices
• Observing topological charges and dynamical bulk-surface correspondence with ultracold atoms
• Gate-Tunable Fractional Chern Insulators in Twisted Double Bilayer Graphene
• Detecting fractional Chern insulators through circular dichroism
• Floquet analysis of a quantum system with modulated periodic driving
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Topological bands with Chern number C=2 by dipolar exchange interactions
• Topological states in multi-orbital HgTe honeycomb lattices
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices
• Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
• Quantum Metric Induced Phases in Moiré Materials
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Desiging Artificial Lieb Lattice on Metal Surface
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Crystal Net Catalog of Model Flat Band Materials
• Magnon crystallization in the kagome lattice antiferromagnet
• Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers
• Non-Hermitian Mott Skin Effect
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Delta chain with ferromagnetic and antiferromagnetic interactions at the critical point
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• Topological Lattice Models with Constant Berry Curvature
• Exceptional band touching for strongly correlated systems in equilibrium
• Fractional Chern insulators with strong interactions far exceeding bandgaps
• Bosonic integer quantum Hall effect in optical flux lattices
• Creating anomalous Floquet Chern insulators with magnetic quantum walks
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Phase transitions out of quantum Hall states in moiré materials
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Dissipation-induced topological insulators: A no-go theorem and a recipe
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Model Fractional Chern Insulators
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Parent Berry curvature and the ideal anomalous Hall crystal
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation
• Three-level Haldane-like model on dice optical lattice
• Circuit Quantum Electrodynamics Simulator of Flat Band Physics in Lieb lattice
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Flatband Line States in Photonic Super-Honeycomb Lattices
• Flat-band localization and interaction-induced delocalization of photons
• Phase diagram topology of the Haldane-Hubbard-Coulomb model
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Twisted bilayer graphene in a parallel magnetic field
• Recent Developments in Fractional Chern Insulators
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Jahn-Teller effect in systems with strong on-site spin-orbit coupling
• Electron-Phonon Interactions in Flat Band Systems
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Charge excitation dynamics in bosonic fractional Chern insulators
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Detecting Topological Phases of Microwave Photons in a Circuit Quantum Electrodynamics Lattice
• Characterization of quasiholes in fractional Chern insulators
• Flat bands and long range Coulomb interactions: conducting or insulating?
• Flat Topological Bands and Eigenstate Criticality in a Quasiperiodic Insulator
• Compact Discrete Breathers on Flat Band Networks
• Flat-band-based multifractality in the all-band-flat diamond chain
• Probing photon correlations in the dark sites of geometrically frustrated cavity lattices
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Fractional Excitonic Insulator
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Evolution of Floquet Topological Quantum States in Driven Semiconductors
• Hidden mechanism for embedding the flat bands of Lieb, kagome, and checkerboard lattices in other structures
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Topology and localization of a periodically driven Kitaev model
• Two-component quantum Hall effects in topological flat bands
• Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement
• Coupled Atomic Wires in a Synthetic Magnetic Field
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• Localization and criticality in antiblockaded 2D Rydberg atom arrays
• Fractional Chern insulators with a non-Landau level continuum limit
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Thermodynamic properties of Ba${}_2$CoSi${}_2$O${}_6$Cl${}_2$ in strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet
• Interacting bosons in topological optical flux lattices
• Systematic construction of topological flat-band models by molecular-orbital representation
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Creating a bosonic fractional quantum Hall state by pairing fermions
• Quasiparticles, Flat Bands, and the Melting of Hydrodynamic Matter
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Higher vortexability: zero field realization of higher Landau levels
• Strain induced superconductor-insulator transition on Lieb lattice
• Fractional Chern Insulators in Bands with Zero Berry Curvature
• Influence of interactions on the anomalous quantum Hall effect
• Doping a fractional quantum anomalous Hall insulator
• Non-Compact Atomic Insulators
• Fate of exceptional points under interactions: Reduction of topological classifications
• SU(N) fractional quantum Hall effects in topological flat bands
• Dissipative preparation of fractional Chern insulators
• Flat-band spin dynamics and phonon anomalies of the saw-tooth spin-chain system Fe${}_2$O(SeO${}_3$)${}_2$
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Archetypical "push the band critical point" mechanism for peaking of the density of states in three-dimensional crystals: Theory and case study of cubic H${}_3$S
• Interference of the Bloch phase in layered materials with stacking shifts
• Behavior of Floquet Topological Quantum States in Optically Driven Semiconductors
• Local incompressibility estimates for the Laughlin phase
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Superconducting circuit simulator of Bose-Hubbard model with a flat band
• SmO thin films: a flexible route to correlated flat bands with nontrivial topology
• Metal-insulator transition in infinitesimally weakly disordered flatbands
• Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
• Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Fractional Chern Insulators in Singular Geometries
• Localized modes in nonlinear fractional systems with deep lattices
• Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands
• Excitonic fractional quantum Hall hierarchy in Moiré heterostructures
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Probing the Flat Band of Optically-Trapped Spin-Orbital Coupled Bose Gases Using Bragg Spectroscopy
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Flat-band ferromagnetism in a topological Hubbard model
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Topological inverse Anderson insulator
• Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
• Skyrmion quantum spin Hall effect
• Correlations and entanglement in flat band models with variable Chern numbers
• Honeycomb-Lattice Mott insulator on Tantalum Disulphide
• Necessary and sufficient conditions for flat bands in $M$-dimensional $N$-band lattices with complex-valued nearest-neighbour hopping
• Strongly interacting photons in 2D waveguide QED
• Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder
• Magnetization process and low-temperature thermodynamics of a spin-1/2 Heisenberg octahedral chain
• Hyperbolic Fractional Chern insulators
• Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Fractional Chern insulator edges and layer-resolved lattice contacts
• Fractional Quantum Hall States of Dipolar Gases in Chern Bands
• Topological Properties of τ-Type Organic Conductors with a Checkerboard Lattice
• Higher angular momentum band inversions in two dimensions
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Compact localised states in magnonic Lieb lattices
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Conductance transition with interacting bosons in an Aharonov-Bohm cage
• Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide
• Dynamical Generation of Topological Magnetic Lattices for Ultracold Atoms
• $SU(3)$ Topological Insulators in the Honeycomb Lattice
• Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
• Topologically non-trivial Hofstadter bands on the kagome lattice
• Domain-wall topology induced by spontaneous symmetry breaking in polariton graphene
• Infinite bound states and hydrogen atom-like energy spectrum induced by a flat band
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Quantum Anomalous Hall Insulator of Composite Fermions
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Correlation functions and characteristic lengthscales in flat band superconductors
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Tunable and direction-dependent group velocities in topologically protected edge states
• Topological insulators with arbitrarily tunable entanglement
• Two-dimensional topological order of kinetically constrained quantum particles
• Broken Symmetry in Ideal Chern Bands
• A continuous family of fully-frustrated Heisenberg model on the Kagome lattice
• Observation of a flat and extended surface state in a topological semimetal
• Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band
• Quasielectrons in lattice Moore-Read models
• Optical anisotropy of the kagome magnet FeSn: Dominant role of excitations between kagome and Sn layers
• One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Exact Topological Flat Bands from Continuum Landau Levels
• Response of fermions in Chern bands to spatially local quenches
• Moiré semiconductors on twisted bilayer dice lattice
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• RKKY interaction in one-dimensional flat-band lattices
• Evolution between quantum Hall and conducting phases: simple models and some results
• Exploration of trivial and non-trivial electronic phases and of collinear and non-collinear magnetic phases in low-spin d${}^5$ perovskites
• Compact Wannier Functions in One Dimension
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Quantum Hall effects of exciton condensate in topological flat bands
• Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Flat bands without twists: periodic holey graphene
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
• Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems
• Mapping a fractional quantum Hall state to a fractional Chern insulator
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Interplay of many-body interactions and quasiperiodic disorder in the all-band-flat diamond chain
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Parafermions in Moiré Minibands
• Simulating chiral spin liquids with projected entangled-pair states
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Quantum mechanics of composite fermions
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Zero-energy excitation in the classical kagome antiferromagnet NaBa${}_2$Mn${}_3$F${}_{11}$
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Hybrid Interference Induced Flat Band Localization in Bipartite Optomechanical Lattices
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Topological charge pumping with subwavelength Raman lattices
• Properties of Laughlin states on fractal lattices
• Reordering Fractional Chern Insulators into Stripes of Fractional Charges with Long-Range Interactions
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Coexisting Kagome and Heavy Fermion Flat Bands in YbCr${}_6$Ge${}_6$
• From Frustrated to Unfrustrated: Coupling two triangular-lattice itinerant Quantum Magnets
• Anomalous Bilayer Quantum Hall Effect
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Continuum limit of lattice quasielectron wavefunctions
• Sawtooth lattice multiferroic BeCr${}_2$O${}_4$: Non-collinear magnetic structure and multiple magnetic transitions
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems
• Anomalous magnetic transport and extra quantum oscillation in semi-metallic photon-like fermion gas
• Mott transition and magnetism in a fragile topological insulator
• Selective band interaction and long-range hopping in a structured environment with giant atoms
• Geometric transport signatures of strained multi-Weyl semimetals
• One-dimensional Dexter-type excitonic topological phase transition
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Symmetry-protected flatband condition for Hamiltonians with local symmetry
• Topological Triviality of Flat Hamiltonians
• Kerr and Faraday rotations in topological flat and dispersive band structures
• Correlation-driven non-trivial phases in single bi-layer Kagome intermetallics
• Universal Performance Gap of Neural Quantum States Applied to the Hofstadter-Bose-Hubbard Model
• Topological phase transition and its stability against an applied magnetic field in a class of low dimensional decorated lattices
• Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice
• Robust Orbital-Selective Flat Bands in Transition-Metal Oxychlorides
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Robustness of real-space topology in moiré systems
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Exceptional flat bands in bipartite non-Hermitian lattices
• Non-ergodic one-magnon magnetization dynamics of the kagome lattice antiferromagnet
• Chains of nanoparticles for flat-band emission and lasing
• Influence of flat bands on RKKY interaction: perspective of Fano defects
• Phase transitions of the dimerized Kane-Mele model with/without the strong interaction
• Generalizing the composite fermion theory for fractional Chern insulators
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• Topological Order Without Band Topology in Moiré Graphene
• Evolution of the optimal trial wave function with interactions in fractional Chern insulators
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain
• Invisible flat bands on a topological chiral edge
• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
• Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals
• Flux attachment theory of fractional excitonic insulators
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• Flat band mediated photon-photon interactions in 2D waveguide QED networks
• Ferromagnetic--nematic order and strongly correlated phases of fermions in optical flux lattices
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction