| We show that orbital degrees of freedom in frustrated lattice systems lead to a narrowing of topologically nontrivial bands. We then show that the t_-orbital manifold near half filling supports a spin-chiral magnetic ordering pattern on the triangular lattice. Itinerant electrons moving in this spin background effective have topologically non-trivial and nearly flat bands. We then study potential fractional Chern insulating (FCI) states, i.e. lattice analogs to fractional quantum Hall states, their robustness with respect to disorder and their competition with a charge-density wave (CDW). As the CDW is rather sensitive to nesting of the Fermi surface, FCI states are far more easily induced in the absence of nesting. While very flat bands are indeed favorable to FCI states, poorly nested dispersive bands are better than nested flatter bands. |
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