Divergent Coulomb screening in two dimensional electron gas driven by microwaves

Two dimensional electron gas in perpendicular magnetic field, driven by microwave $ac$- field is studied. The magneto-conductivity and the diffusion constant are calculated in the microscopic model. In the driven state the Einstein relation is violated. Instability of the Coulomb screening and a divergence of the effective donor electrostatic field due to the negative Ryzhii currents is predicted. This phenomenon results in the zero-resistance states observed experimentally.