Floquet analysis of excitations in materials

Controlled excitation of materials can transiently induce changed or novel properties with many fundamental and technological implications. Especially, the concept of Floquet engineering and the manipulation of the electronic structure via dressing with external lasers have attracted some recent interest. Here we review the progress made in defining Floquet material properties and give a special focus on their signatures in experimental observables as well as considering recent experiments realizing Floquet phases in solid state materials. We discuss how a wide range of experiments with non-equilibrium electronic structure can be viewed by employing Floquet theory as an analysis tool providing a different view of excitations in solids.