Optical response of Floquet topological insulators

Optical probes provide detailed information about electronic excitations in equilibrium, but a new formulation is needed to understand their utility in nonequilibrium Floquet system. Motivated to find useful signatures of Floquet topological phases, we formulate a linear response theory for a Floquet system subjected to an external field and derive the generalized optical conductivity. We recover Kubo or Floquet optical Hall conductivity previously discussed in the literature in appropriate limits. In a Floquet system, optical conductivity acquires a Fourier decomposition, describing the response to a probe frequency displaced by the harmonics of the drive frequency. We obtain analytical results and perform numerical calculations for different scenarios of the occupation of the bands, in particular, the diagonal Floquet distribution and the distribution obtained after a quench. We discuss the structure of optical Hall and longitudinal conductivity in different topological phases.