Fractional Chern Insulators in Bands with Zero Berry Curvature

TL;DR

This paper demonstrates that fractional Chern insulators can be stabilized in bands with zero Berry curvature through interactions that break time-reversal symmetry, with both theoretical and numerical evidence supporting the feasibility of such states.

Contribution

It introduces methods to stabilize fractional Chern insulators in zero Berry curvature bands and shows their viability even with short-range interactions.

Findings

Fractional Chern insulators can exist in zero Berry curvature bands.

Interactions that break time-reversal symmetry are key to stabilizing these states.

Numerical evidence supports the stability of fractional Chern insulators with short-range interactions.

Abstract

Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilise a fractional Chern insulator. These interactions necessarily break time-reversal symmetry (either spontaneously or explicitly) and have the effect of altering the underlying band structure. We outline a number of ways in which this may be achieved, and show how similar interactions may also be used to create a (time-reversal symmetric) fractional topological insulator. While our approach is rigorous in the limit of long range interactions, we show numerically that even for short range interactions a fractional Chern insulator can be stabilised in a band with zero Berry curvature.