Topological flat band models with arbitrary Chern numbers

Abstract

We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an $N$-band square lattice model with $C=N$ for an arbitrary integer $N$. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C=2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall state is observed.

8 pages, 7 figures

References in corpus (28)

• 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
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Nearly flat band with Chern number C=2 on the dice lattice
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Zoology of Fractional Chern Insulators
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Flat bands with higher Chern number in pyrochlore slabs
• Fractional topological phases and broken time reversal symmetry in strained graphene
• Fractional quantum-Hall liquid spontaneously generated by strongly correlated t_2g electrons
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Narrowing of topological bands due to electronic orbital degrees of freedom
• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros

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• Exotic electronic states in the world of flat bands: from theory to material
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• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Hierarchy of fractional Chern insulators and competing compressible states
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Towards large-Chern-number topological phases by periodic quenching
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Repulsive Casimir Effect with Chern insulators
• Distant-Neighbor Hopping in Graphene and Haldane Models
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• Topological quantum optics using atom-like emitter arrays coupled to photonic crystals
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Parity-time symmetry in a flat band system
• Compact localized states and flat bands from local symmetry partitioning
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• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
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• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• Bosonic integer quantum Hall effect in optical flux lattices
• Fractional Quantum Hall States of Rydberg Polaritons
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• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
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• 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
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• Interacting bosons in topological optical flux lattices
• Flat bands with band crossings enforced by symmetry representation
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Anomalous Coherence Length in Superconductors with Quantum Metric
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Topological features of Haldane model on a dice lattice: role of flat band on transport properties
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• New insight into tuning magnetic phases of $R$Mn${}_6$Sn${}_6$ kagome metals
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• Floquet High Chern Insulators in Periodically Driven Chirally Stacked Multilayer Graphene
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• High-Chern number phase in the topological insulator multilayer structures
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• Correlations and entanglement in flat band models with variable Chern numbers
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
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• Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
• Individual band with higher Chern numbers in double perovskite {001} monolayers
• 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
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Geometric and conventional contributions of superconducting diode effect: Application to flat-band systems
• Band engineered bilayer Haldane model: Evidence of multiple topological phase transitions
• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
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