“Floquet engineering” - designing band structures “on-demand" through an application of coherent time-periodic drives, has recently emerged as a powerful tool for inducing exotic phenomena in ordinary materials. In this talk, I will discuss the application of Floquet engineering for inducing novel non-equilibrium phases of matter in steady states of time-periodically driven semiconductors. The steady states are achieved due to the interplay between the coherent external drive, electron-electron interactions, and dissipative processes arising from the coupling to phonons and the electromagnetic environment. I will show that despite the highly non-equilibrium nature of these systems, by judicially choosing the properties of the material, the external drive, and the environments, their steady states can exhibit topological transport, metal-to-insulator phase transitions and even strongly correlated phases such as a novel electronic liquid gyro-crystalline phase.

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