Chern-Simons Composite Fermion Theory of Fractional Chern Insulators

Abstract

We formulate a Chern-Simons composite fermion theory for Fractional Chern Insulators (FCIs), whereby bare fermions are mapped into composite fermions coupled to a lattice Chern-Simons gauge theory. We apply this construction to a Chern insulator model on the kagome lattice and identify a rich structure of gapped topological phases characterized by fractionalized excitations including states with unequal filling and Hall conductance. Gapped states with the same Hall conductance at different filling fractions are characterized as realizing distinct symmetry fractionalization classes.

14 pages, 7 figures. Expanded version in PRB format with revised mean field analysis (conclusions are essentially unchanged)

References in corpus (10)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice

Cited by in corpus (21)

• Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices
• Fermionization of Bosons in a Flat Band
• Fractional Chern insulators with a non-Landau level continuum limit
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• From frustrated magnetism to spontaneous Chern insulators
• Lattice realization of compact $U(1)$ Chern-Simons theory with exact 1-symmetries
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• 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
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Lattice BF Theory, Dumbbells, and Composite Fermions
• Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
• Abelian Chern-Simons Gauge Theory on The Lattice
• A Two-Gauge Field Model for Magnetoelectric Boundaries
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Generalizing the composite fermion theory for fractional Chern insulators
• Topological Order Without Band Topology in Moiré Graphene
• Theory of Hofstadter Superconductors