Fractional Chern Insulators in Bands with Zero Berry Curvature

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.

7 pages, 2 figures; Published version

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• Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems
• Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Exciton fractional Chern insulators in moiré heterostructures
• Robustness of real-space topology in moiré systems
• Generalizing the composite fermion theory for fractional Chern insulators
• Topological Order Without Band Topology in Moiré Graphene