  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.
