Fractional Quantum Hall Effect in Topological Flat Bands with Chern   Number Two
  Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\nu=1/3$ filling characterized by three-fold quasi-degeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\nu=1/5$ filling with short-range interactions. 
Yi-Fei Wang, Hong Yao, Chang-De Gong, D. N. Sheng
cond-mat.str-el cond-mat.mes-hall cond-mat.quant-gas quant-ph