Effective Floquet Hamiltonian in the low-frequency regime

We develop a theory to derive effective Floquet Hamiltonians in the weak-drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially periodic and weak potential, such as occurs in some crystalline materials. As a prototypical example, we apply this theory to graphene driven by circularly polarized light of low intensity. We find an analytic expression for the effective Floquet Hamiltonian in the low-frequency regime which accurately predicts the quasienergy spectrum and the Floquet states. Furthermore, we identify self-consistency as the crucial feature effective Hamiltonians in this regime need to satisfy to achieve high accuracy. The method is useful in providing a realistic description of off-resonant drives for multiband solid-state systems where light-induced topological band structure changes are sought.