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arXiv · 1309.1698

Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers

Ying-Hai Wu·J. K. Jain·Kai Sun
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Abstract

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed "topological nematic states," in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in $C>1$ flat bands and provides some hints on how to realize such states in experiments.

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Ying-Hai Wu, J. K. Jain, Kai Sun. 2013-09-06. Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers. https://doi.org/10.1103/physrevb.91.041119

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