  We investigate the dynamics of a two-dimensional electron gas (2DEG) under
circular polarized microwave radiation in presence of dilute localized
impurities. Inspired by recent developments on Floquet topological insulators
we obtain the Floquet wavefunctions of this system which allow us to predict
the microwave absorption and charge density responses of the electron gas, we
demonstrate how these properties can be understood from the underlying
semiclassical dynamics even for impurities with a size of around a magnetic
length. The charge density response takes the form of a rotating charge density
vortex around the impurity that can lead to a significant renormalization of
the external microwave field which becomes strongly inhomogeneous on the scale
of a cyclotron radius around the impurity. We show that this in-homogeneity can
suppress the circular polarization dependence which is theoretically expected
for MIRO but which was not observed in MIRO experiments on semiconducting
2DEGs. Our explanation, for this so far unexplained polarization independence,
has close similarities with the Azbel'-Kaner effect in metals where the
interaction length between the microwave field and conduction electrons is much
smaller than the cyclotron radius due to skin effect generating harmonics of
the cyclotron resonance.
