Chern-Simons Composite Fermion Theory of Fractional Chern Insulators

TL;DR

This paper develops a Chern-Simons composite fermion theory for Fractional Chern Insulators, revealing a variety of topological phases with fractionalized excitations on the kagome lattice.

Contribution

It introduces a novel composite fermion framework for FCIs using lattice Chern-Simons gauge theory, uncovering new topological phases and symmetry fractionalization classes.

Findings

Identification of multiple gapped topological phases

States with fractional Hall conductance and filling fractions

Distinct symmetry fractionalization classes for same Hall conductance

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.