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We investigate the dynamics of a two-dimensional electron gas (2DEG) undercircular polarized microwave radiation in presence of dilute localizedimpurities. Inspired by recent developments on Floquet topological insulatorswe obtain the Floquet wavefunctions of this system which allow us to predictthe microwave absorption and charge density responses of the electron gas, wedemonstrate how these properties can be understood from the underlyingsemiclassical dynamics even for impurities with a size of around a magneticlength. The charge density response takes the form of a rotating charge densityvortex around the impurity that can lead to a significant renormalization ofthe external microwave field which becomes strongly inhomogeneous on the scaleof a cyclotron radius around the impurity. We show that this in-homogeneity cansuppress the circular polarization dependence which is theoretically expectedfor MIRO but which was not observed in MIRO experiments on semiconducting2DEGs. Our explanation, for this so far unexplained polarization independence,has close similarities with the Azbel'-Kaner effect in metals where theinteraction length between the microwave field and conduction electrons is muchsmaller than the cyclotron radius due to skin effect generating harmonics ofthe cyclotron resonance.

Floquet theory of microwave absorption by an impurity in two dimensional electron gas