Nearly-flat bands with nontrivial topology

Abstract

We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Due to the similarity with 2D continuum Landau levels, these topologically nontrivial nearly-flat bands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flat band aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

4 pages, 3 figures, Supplementary materials added

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• Topological states in two-dimensional optical lattices
• Unconventional superfluid order in the $F$-band of a bipartite optical square lattice
• Orbital order in Mott insulators of spinless p-band fermions
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands
• Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices
• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field

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• Topological flat bands in optical checkerboard-like lattices
• Hyperbolic Fractional Chern insulators
• Interaction effects on almost flat surface bands in topological insulators
• Novel Electronic Structure of Nitrogen-Doped Lutetium Hydrides
• Unconventional delocalization in a family of 3D Lieb lattices
• Methods for the construction of interacting many-body Hamiltonians with compact localized states in geometrically frustrated clusters
• Interacting topological mirror excitonic insulator in one dimension
• Hard-core bosons in one-dimensional interacting topological bands
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Flat bands with local Berry curvature in multilayer graphene
• Fractional Quantum Hall States of Dipolar Gases in Chern Bands
• Classification of Lifshitz invariant in multiband superconductors: an application to Leggett modes in the linear response regime in Kagome lattice models
• Methods for constructing parameter-dependent flat band lattices
• The scaling behavior of the insulator to plateau transition in topological band model
• 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
• Charge-Neutral Electronic Excitations in Quantum Insulators
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Superconductivity with intrinsic topological order induced by pure Coulomb interaction and time-reversal symmetry breaking
• Ferromagnetism and Antiferromagnetism of Correlated Topological Insulator with Flat Band
• 1D flat bands in phosphorene nanoribbons with pentagonal nature
• Correlation driven near-flat band Stoner excitations in a Kagome magnet
• Order-by-Disorder Degeneracy Lifting of Interacting Bosons on the Dice Lattice
• Chern band insulators in magnetic field
• Electron correlations and $T$-breaking density wave order in a ${\mathbb{Z}}_2$ kagome metal
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Fragility of the fractional quantum spin Hall effect in quantum gases
• Nature of continuous phase transitions in interacting topological insulators
• Anomalous geometric transport signatures of topological Euler class
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Two elementary band representation model, Fermi surface nesting, and surface topological superconductivity in $A$V${}_3$Sb${}_5$ ($A=\text{K, Rb, Cs}$)
• Domain-wall topology induced by spontaneous symmetry breaking in polariton graphene
• Bosonic edge states in gapped honeycomb lattices
• Interaction-induced conductance from zero modes in a clean magnetic graphene waveguide
• Fermionic non-Abelian fractional Chern insulators from dipolar interactions
• Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
• Cluster-Based Haldane States in Spin-1/2 Cluster Chains
• Quantum Anomalous Hall Insulator of Composite Fermions
• Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
• Inertial spin waves in spin spirals
• Magnetoresistance signature of two-dimensional electronic states in Co${}_3$Sn${}_2$S${}_2$
• 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
• Non-Abelian Fractional Chern Insulator in Disk Geometry
• Delocalization of edge states in topological phases
• Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands
• Orbital-Active Dirac Materials from the Symmetry Principle
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• On the zero-field quantization of the anomalous quantum Hall effect in moiré 2D layers
• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation
• Spin-dependent $\pi$${\pi }^{\ast }$ gap in graphene on a magnetic substrate
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Spin waves and orbital contribution to ferromagnetism in a topological metal
• Topological insulators with arbitrarily tunable entanglement
• Effective theory of fractional topological insulators in two spatial dimensions
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Broken Symmetry in Ideal Chern Bands
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Aharonov-Bohm effect in a helical ring with long-range hopping: Effects of Rashba spin-orbit interaction and disorder
• Universal Wilson Loop Bound of Quantum Geometry
• Higher-Order Van Hove Singularities in Kagome Topological Bands
• A mono-atomic orbital-based 1D topological crystalline insulator
• Programmable Hamiltonian engineering with quadratic quantum Fourier transform
• Observation of a flat and extended surface state in a topological semimetal
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Chirality-2 fermion induced anti-Klein tunneling in 2D checkerboard lattice
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• Quarter-Filled Honeycomb Lattice with a Quantized Hall Conductance
• Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe${}_2$
• Electrical and thermal transport through $\alpha -T_3$ NIS junction
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Quantum Hall effects of exciton condensate in topological flat bands
• Origin of competing charge density waves in kagome metal ScV${}_6$Sn${}_6$
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Flat-band hybridization between $f$ and $d$ states near the Fermi energy of SmCoIn${}_5$
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Fractional quantum Hall effect of Bose-Fermi mixtures
• Topological quantum phase transition in Kane-Mele-Kondo lattice model
• Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems
• Flux modulated flat band engineering in square-kagome ladder network
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Designing single and degenerate flat bands in the kagome lattice with long-range hopping
• A Passage to Topological Matter: Colloquium
• Charge and spin fractionalization in strongly correlated topological insulators
• Elf autoencoder: unsupervised exploration of flat-band materials using electronic band structure fingerprints
• Engineering flux-controlled flat bands and topological states in a Stagome lattice
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
• Parafermions in Moiré Minibands
• Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Impurity-induced thermal crossover in fractional Chern insulators
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Pairing instabilities in topological insulator quantum wells
• Mapping a fractional quantum Hall state to a fractional Chern insulator
• 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
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Non-perturbative dynamics of flat-band systems with correlated disorder
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Non-trivial Topological Phases on the Stuffed Honeycomb Lattice
• Analytical study of quasi-one dimensional flat band networks and slow light analogue
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Bilayer twisting as a mean to isolate connected flat bands in a Kagome lattice through Wigner crystallization
• van Hove Singularity-Driven Emergence of Multiple Flat Bands in Kagome Superconductors
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Quantum Anomalous Hall Effect in $d$-Electron Kagome Systems: Chern Insulating States from Transverse Spin-Orbit Coupling
• Atomic Layer Molecular Beam Epitaxy of Kagome Magnet RMn${}_6$Sn${}_6$ (R = Er, Tb) Thin Films
• Type-II Dirac Nodal Lines in double-kagome-layered CsV${}_8$Sb${}_{12}$
• 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
• Observation of Resonance of Kagome Flat Band Doublet
• Exact diagonalization of quantum lattice models on coprocessors
• Reordering Fractional Chern Insulators into Stripes of Fractional Charges with Long-Range Interactions
• Superlattice induced electron percolation within a single Landau level
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Flat-band ferromagnetism in a correlated topological insulator on a honeycomb lattice
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Crystalline invariants of fractional Chern insulators
• Viewpoint: Toward Fractional Quantum Hall physics with cold atoms
• Interband excitations in the 1D limit of two-band fractional Chern insulators
• Wavefunction Vortex Attachment via Matrix Products: Application to Atomic Fermi Gases in Flat Spin-Orbit Bands
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Holographic Lieb lattice and gapping its Dirac band
• Double-layer Kagome Metals Pt3Tl2 and Pt3In2
• Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
• Anomalous magnetic transport and extra quantum oscillation in semi-metallic photon-like fermion gas
• Intra-cell dynamics and cyclotron motion without magnetic field
• Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model
• Topological Triviality of Flat Hamiltonians
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Interaction-driven plateau transition between integer and fractional Chern Insulators
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Three-component fractional quantum Hall effect in topological flat bands
• Chiral spin liquid from magnetic Wannier states
• Magnetism of kagome metals $\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)\text{Sn}$ studied by $\mu$SR
• Optical signatures of -1/3 fractional quantum anomalous Hall state in twisted MoTe2
• Robust Orbital-Selective Flat Bands in Transition-Metal Oxychlorides
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Dichotomy of flat bands in the van der Waals ferromagnet Fe${}_5$GeTe${}_2$
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Kerr and Faraday rotations in topological flat and dispersive band structures
• 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
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Mott Insulator-Superfluid Transition in a Generalized Bose-Hubbard Model with Topologically Non-trivial Flat-Band
• Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy
• Inter-species topological phases via a dynamical gauge field
• Non-Abelian line graph: A generalized approach to flat bands
• Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators
• Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
• Frustration-free free fermions
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Floquet-Engineered Valley-Topotronics in Kekulé-Y Bond Textured Graphene Superlattice
• Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Proximity-induced flat bands and topological properties in a decorated diamond chain
• Investigating the Electrical Transport Properties and Electronic Structure of Zr2CuSb3
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• General Many-Body Perturbation Framework for Moiré Systems
• Topological Order Without Band Topology in Moiré Graphene
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Topologically nontrivial flat bands and quantum Hall crossovers in square-octagon lattice materials
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Flux attachment theory of fractional excitonic insulators
• RKKY couplings in the Lieb lattice: flat-band induced frustration
• 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${}_2$
• A theorem regarding families of topologically non-trivial fermionic systems
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Flux-induced strengthening of the magnetic couplings in a flat-band diamond chain
• Zero Indirect Band Gap and Flat Bands in a Niobium Oxyiodide Cluster Material
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Evolution from Topological Dirac Metal to Flat-band-Induced Antiferromagnet in Layered KxNi4S2 (0<=x<=1)
• Evolution of the optimal trial wave function with interactions in fractional Chern insulators
• Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State
• Dissipation-Driven Transition of Particles from Dispersive to Flat Bands
• Orbital Description of Landau Levels
• Flat band mediated photon-photon interactions in 2D waveguide QED networks
• Topological phases of monolayer and bilayer depleted Lieb lattices
• Exact Mappings in Condensed Matter Physics
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Theory of Hofstadter Superconductors
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings