Optical Conductivity Signatures of Floquet Electronic Phases

Optical conductivity measurements may provide access to distinct signatures of Floquet electronic phases, which are described theoretically by their quasienergy band structures. Here, we focus on characterizing experimental observables of the Floquet graphene antidot lattice, which we introduced previously [Phys. Rev. B 104, 174304 (2021)]. On the basis of Floquet linear response theory, the real and imaginary parts of the longitudinal and Hall optical conductivity are computed as a function of probe frequency. We find that the number and positions of peaks in the response function are distinctive of the different Floquet electronic phases, and identify multiple properties with no equilibrium analog. First, for several intervals of probe frequencies, the real part of the conductivity becomes negative, which we argue is indicative of negative Joule heating. That is, the Floquet drive causes the material to amplify the power of the probe (gain). Additionally, while there is zero Hall response at equilibrium, the real and imaginary parts of the Floquet Hall conductivity are non-zero and can be as large as the longitudinal components. Lastly, driving-induced localization tends to reduce the overall magnitude of and to flatten out the optical conductivity signal. From an implementation standpoint, a major advantage of the antidot lattice is that the above-bandwidth driving limit is reached with photon energies that are at least twenty times lower than that required for the intrinsic material, allowing for significant band renormalization at orders-of-magnitude smaller intensities. Our work provides the necessary tools for experimentalists to map reflectance data to particular Floquet phases for this novel material.