Floquet Topological Phases

Periodically driven quantum systems host "Floquet-Bloch" bands — defined by the time-evolution operator over one drive period. Unlike static systems, Floquet insulators can have non-trivial winding numbers at BOTH quasi-energy gaps (0 and π), enabling anomalous edge modes. Tune the drive amplitude to cross topological phase transitions.

Floquet systems: H(t+T)=H(t). The Floquet operator U=Te^{-i∫H dt} has eigenvalues e^{-iεT} where ε∈(-π/T,π/T] is quasi-energy. Non-trivial winding number → topologically protected edge states.