From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect

Abstract

We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron systems in a strong magnetic field.

8 pages, 3 figure; published version with labels in Figs. 2 and 3 corrected

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional Chern Insulator
• Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands
• Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Topological insulators and fractional quantum Hall effect on the ruby lattice

Cited by in corpus (50)

• Topological Flat Band Models and Fractional Chern Insulators
• Band geometry of fractional topological insulators
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• Geometric stability of topological lattice phases
• Hierarchy of fractional Chern insulators and competing compressible states
• Band structure engineering of ideal fractional Chern insulators
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Magnetic crystals and helical liquids in alkaline-earth fermionic gases
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Noncommutative geometry for three-dimensional topological insulators
• Fractional Chern Insulators beyond Laughlin states
• Topological states in multi-orbital HgTe honeycomb lattices
• Adiabatic continuity between Hofstadter and Chern insulator states
• Quantum Metric Induced Phases in Moiré Materials
• Hamiltonian theory of fractionally filled Chern bands
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Topological Lattice Models with Constant Berry Curvature
• Fractional Chern insulator on a triangular lattice of strongly correlated $t_{2g}$ electrons
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Observation of the dual quantum spin Hall insulator by density-tuned correlations in a van der Waals monolayer
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• D-Algebra Structure of Topological Insulators
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Interacting bosons in topological optical flux lattices
• Edge Excitations in Fractional Chern Insulators
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Flat-band ferromagnetism in a topological Hubbard model
• Probing fractional topological insulators with magnetic edge perturbations
• Tuning the topological insulator states of artificial graphene
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
• Topological BF theory of the quantum hydrodynamics of incompressible polar fluids
• Fragility of the fractional quantum spin Hall effect in quantum gases
• Effective theory of fractional topological insulators in two spatial dimensions
• Broken Symmetry in Ideal Chern Bands
• Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a $\pi$-flux Dice Lattice with Flat Bands
• Parafermions in Moiré Minibands
• Weyl Semimetal and Nonassociative Nambu Geometry
• Excitonic gap generation in thin-film topological insulators
• On the geometrical description of fractional Chern insulators based on static structure factor calculations