Comment on "Floquet Fractional Chern Insulators"

TL;DR

This paper critiques a previous study on Floquet fractional Chern insulators, highlighting missing terms in the Floquet Hamiltonian calculation and questioning the assumptions about band filling in driven systems.

Contribution

It provides a critical analysis of the prior work, identifying potential inaccuracies in the derivation of the Floquet Hamiltonian and assumptions about electron filling.

Findings

Missing terms of order ω^{-1} in the Floquet Hamiltonian calculation.

Questioning the validity of band filling assumptions in driven systems.

Highlights the need for more precise theoretical treatment.

Abstract

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.