Nonlinear current of strongly irradiated quantum Hall gas

Two dimensional electrons in weakly disordered high Landau levels are considered. The current-field response in the presence of a strong microwave field is computed. The disordered Floquet evolution operator allows us to treat the short range disorder perturbatively, at any strength of electric fields. A simplifying random matrix approximation reproduces the broadened Landau level density of states and structure factor. We derive the magnitude of the microwave induced resistivity oscillations. The disorder short wavelength cutoff determines the nonlinear electric fields of the zero resistance state and the Hall induced resistivity oscillations. We discuss wider implications of our results on experiments and other theories.