Comment on "Floquet Fractional Chern Insulators"

In a recent paper [Phys. Rev. Lett. 112 156801 (2014)], Grushin et al. studied a Fermi-Hubbard-model for spinful electrons on a honeycomb lattice coupled to an external polarized electric field. By computing the Floquet Hamiltonian perturbatively to order $\omega^{-1}$ (where $\omega$ is the frequency of the drive) they predicted that, for specific values of the driving and filling, the system can transition into a Fractional Chern Insulator. In this comment we point out that: i) the calculation of the Floquet Hamiltonian misses some terms of order $\omega^{-1}$ and ii) the assumption that the Floquet bands are filled as in time-independent systems is questionable.