Fractional Chern insulators in bands with zero Berry curvature

Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilize 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 stabilized in a band with zero Berry curvature.