Adiabatic continuity between Hofstadter and Chern insulator states

Abstract

We show that the topologically nontrivial bands of Chern insulators are adiabatic cousins of the Landau bands of Hofstadter lattices. We demonstrate adiabatic connection also between several familiar fractional quantum Hall states on Hofstadter lattices and the fractional Chern insulator states in partially filled Chern bands, which implies that they are in fact different manifestations of the same phase. This adiabatic path provides a way of generating many more fractional Chern insulator states and helps clarify that nonuniformity in the distribution of the Berry curvature is responsible for weakening or altogether destroying fractional topological states.

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Cited by in corpus (49)

• Topological Flat Band Models and Fractional Chern Insulators
• Fractional Quantum Hall Physics in Topological Flat Bands
• Correlation effects in two-dimensional topological insulators
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Hierarchy of fractional Chern insulators and competing compressible states
• Band structure engineering of ideal fractional Chern insulators
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Hamiltonian theory of fractionally filled Chern bands
• Creating anomalous Floquet Chern insulators with magnetic quantum walks
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
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• Model Fractional Chern Insulators
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Topological exact flat bands in two dimensional materials under periodic strain
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Wigner crystallization in topological flat bands
• Composite Fermions on a Torus
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Interacting bosons in topological optical flux lattices
• Edge Excitations in Fractional Chern Insulators
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Fractional quantum anomalous Hall effect in a singular flat band
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry
• Floquet engineering of topological phase transitions in quantum spin Hall $\alpha$-$T_3$ system
• Josephson Coupled Moore-Read States
• Fractional Quantum Hall States of Dipolar Gases in Chern Bands
• 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
• Quantum phases of two-component bosons on the Harper-Hofstadter ladder
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
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• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
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• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Chiral spin liquid from magnetic Wannier states
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State
• Exact Mappings in Condensed Matter Physics
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states