Fractional (Chern and topological) insulators

TL;DR

This paper reviews the unique features of interacting topological phases in two dimensions, focusing on fractional Chern insulators and topological insulators, highlighting their stability and fractionalized excitations.

Contribution

It provides a comprehensive review of fractional Chern and topological insulators, emphasizing their distinct properties and challenges to conventional quantum Hall intuition.

Findings

FCIs are stable even when interaction energy exceeds the band gap

FTIs can have fractionalized bulk excitations without gapless edges

The paper clarifies conceptual differences from quantum Hall systems

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.