The paper discusses the creation of a Floquet Topological Insulator (FTI) in semiconductor quantum wells, specifically HgTe/CdTe heterostructures. The authors show that by irradiating these quantum wells with microwave frequencies, a topological state can be induced in a device initially in the trivial phase without closing the gap or crossing a phase transition. The quasi-energy spectrum exhibits a single pair of helical edge states, and the velocity of these edge states can be tuned by adjusting the intensity of the microwave radiation. The proposal provides a proof of principle for a new non-equilibrium topological state, the FTI, which has robust edge modes and other hallmarks of topological phases. The authors also discuss the experimental parameters required to realize this proposal, including the use of electromagnetic radiation in the microwave-THz regime. The work highlights the potential for controlling the spectral properties of edge states and the bandgap of the bulk insulator, as well as the fast formation of FTIs in response to external fields, opening new avenues for studying quench dynamics of topological states in solid-state devices.The paper discusses the creation of a Floquet Topological Insulator (FTI) in semiconductor quantum wells, specifically HgTe/CdTe heterostructures. The authors show that by irradiating these quantum wells with microwave frequencies, a topological state can be induced in a device initially in the trivial phase without closing the gap or crossing a phase transition. The quasi-energy spectrum exhibits a single pair of helical edge states, and the velocity of these edge states can be tuned by adjusting the intensity of the microwave radiation. The proposal provides a proof of principle for a new non-equilibrium topological state, the FTI, which has robust edge modes and other hallmarks of topological phases. The authors also discuss the experimental parameters required to realize this proposal, including the use of electromagnetic radiation in the microwave-THz regime. The work highlights the potential for controlling the spectral properties of edge states and the bandgap of the bulk insulator, as well as the fast formation of FTIs in response to external fields, opening new avenues for studying quench dynamics of topological states in solid-state devices.