# Interpretation of Floquet Band Structure in Multi-band Models

Computing band structures inside Floquet formalism has become quite common, see e.g. [1]. While I think to fully understand it from a mathematical point of view, I'm lacking some physical interpretation. In particular, the thing that has been bothering me, is the following thought:

Imagine a band structure with multiple bands below and above Fermi energy, respectively. Now we compute the band structure in Floquet formalism for some (electromagnetic) perturbation oscillating with frequency $$\omega$$. Assume that one of the bands that was originally well below (or above) the Fermi energy has now been shifted by $$\hbar\omega$$ ($$-\hbar\omega$$), such that it lies right between the original valence and conduction band.

Interpreting the Fourier components of the Floquet formalism as photonic excitations, I think that (assuming the shape of the band structure stays mostly the same) the states directly above/below the original Fermi and with mean "photonic excitation" of $$0$$ are most likely the new valence and conduction band. However, I really don't know whether this interpretation is correct. And, more importantly, I don't know how to interpret this new band between them (or possibly even cutting through the both of them). In fact, I don't even know whether we can even deal with a clear notion of valence and conduction band at all.

Hence, my questions:

• How do we interpret the new bands obtained from Floquet formalism physically?
• Is there still a clear notion of valence and conduction band?
• What would be the meaning of a newly emerging band crossing either (or both) of the two?