Floquet Scattering Theory based on Effective Hamiltonians of Driven Systems

The design of time-independent effective Hamiltonians that describe periodically modulated systems, provides a promising approach to realize new forms of matter. This, so-called, Floquet engineering approach is currently limited to the description of wavepacket dynamics. Here, we utilize the notion of effective Hamiltonians and develop a Floquet engineering scattering formalism that relies on a systematic high-frequency expansion of the scattering matrix. The method unveils the critical role of micromotion. An application to the case of non-reciprocal transport is presented.