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A 2D electron system in a quantized magnetic field can be driven by microwaveradiation into a non-equilibrium state with strong magnetooscillations of thedissipative conductivity. We demonstrate that in such system a negativeconductivity can coexist with a positive diffusion coefficient. In a finitesystem, solution of coupled electrostatic and linear transport problems showsthat the diffusion can stabilize a state with negative conductivity.Specifically, this happens when the system size is smaller than the absolutevalue of the non-equilibrium screening length that diverges at the point wherethe conductivity changes sign. We predict that a negative resistance can bemeasured in such a state. Further, for a non-zero difference between the workfunctions of two contacts, we explore the distribution of the electrostaticpotential and of the electron density in the sample. We show that in thediffusion-stabilized regime of negative conductivity the system splits into tworegions with opposite directions of electric field. This effect is a precursorof the domain structure that has been predicted to emerge spontaneously in themicrowave-induced zero-resistance states.

Negative conductivity and anomalous screening in two-dimensional electron systems subjected to microwave radiation