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Floquet vortex states induced by light carrying the orbital angular momentum

We propose a scheme to create an electronic Floquet vortex state by irradiating a two-dimensional semiconductor with the laser light carrying non-zero orbital angular momentum. We analytically and numerically study the properties of the Floquet vortex states, with the methods analogous to the ones previously applied to the analysis of superconducting vortex states. We show that such Floquet vortex states are similar to the superconducting vortex states, and they exhibit a wide range of tunability. To illustrate the potential utility of such tunability, we show how such states could be used for quantum state engineering.