Optical conductivity and magnetic properties of light-induced Floquet vortex states

In a recent paper (arxiv:2106.08515), it was demonstrated that irradiating light with a non-zero orbital angular momentum on a massive Dirac fermionic insulator can create localized vortex states. In this work, we study physical observables that can reveal the existence of vortex states in these systems. Specifically, the longitudinal and transverse dynamical conductivities are calculated and we separate the contributions of the vortex states to conductivities from those of bulk and edge states. Additionally, the self-induced current density due to the non-vanishing orbital angular momentum of light is evaluated and we calculate its resulting orbital magnetization. We also discuss experimental methods for measuring this orbital magnetization.