Fractional (Chern and topological) insulators

Abstract

We review various features of interacting Abelian topological phases of matter in two spatial dimensions, placing particular emphasis on fractional Chern insulators (FCIs) and fractional topological insulators (FTIs). We highlight aspects of these systems that challenge the intuition developed from quantum Hall physics - for instance, FCIs are stable in the limit where the interaction energy scale is much larger than the band gap, and FTIs can possess fractionalized excitations in the bulk despite the absence of gapless edge modes.

15 pages, no figures, overview for proceedings of Nobel symposium on "New forms of matter: topological insulators and superconductors"

References in corpus (24)

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• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Surface codes: Towards practical large-scale quantum computation
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• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Fractional quantum Hall effect in the absence of Landau levels
• On the $Z_2$ classification of Quantum Spin Hall Models
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Enhancing the stability of a fractional Chern insulator against competing phases
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Interaction driven quantum phase transition in fractional quantum spin Hall effects
• Accessing topological order in fractionalized liquids with gapped edges

Cited by in corpus (60)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Nearly Flat Chern Bands in Moiré Superlattices
• Topological Non-Hermitian skin effect
• Essay: Where Can Quantum Geometry Lead Us?
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Measuring quantized circular dichroism in ultracold topological matter
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Topological flat bands in twisted trilayer graphene
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Creating anomalous Floquet Chern insulators with magnetic quantum walks
• Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe${}_2$
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Model Fractional Chern Insulators
• Multiple Chern bands in twisted MoTe${}_2$ and possible non-Abelian states
• Ultra-Strong Spin-Orbit Coupling and Topological Moiré Engineering in Twisted ZrS2 Bilayers
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Recent Developments in Fractional Chern Insulators
• Charge excitation dynamics in bosonic fractional Chern insulators
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Fractional Excitonic Insulator
• Fractional Chern insulators with a non-Landau level continuum limit
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Quantum Geometric Kohn-Luttinger Superconductivity
• Higher vortexability: zero field realization of higher Landau levels
• Synthetic Flux Attachment
• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• 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
• Higher angular momentum band inversions in two dimensions
• Delta-T noise for fractional quantum Hall states at different filling factor
• Attractive Haldane bilayers for trapping non-Abelian anyons
• 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
• Microscopic Diagnosis of Universal Geometric Responses in Fractional Quantum Hall Liquids
• Textured Exciton Insulators
• Universal Wilson Loop Bound of Quantum Geometry
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• Variational wavefunctions for fractional topological insulators
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Geometric transport signatures of strained multi-Weyl semimetals
• Mott transition and magnetism in a fragile topological insulator
• Candidate for a Fractional Topological Insulator in Twisted MoTe2
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level
• Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems
• Flux attachment theory of fractional excitonic insulators
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Generalizing the composite fermion theory for fractional Chern insulators
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges
• Evolution of the optimal trial wave function with interactions in fractional Chern insulators
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands