Differential resistance of two dimensional electron systems subject to microwave radiation

We present the expression for differential resistance of a disordered two-dimensional electron gas placed in a perpendicular magnetic field and subject to microwave irradiation. We demonstrate that in strong dc electric fields the current oscillates as a function of the strength of the applied constant electric field. We demonstrate that the amplitude of oscillations of the differential resistivity is characterized by the back-scattering rate off disorder. We argue that the dominant contribution to the non-linearity in strong electric fields originates from the modification of electron scattering off disorder by electric fields, or so-called "displacement" mechanism. The non-equilibrium mechanism, which is related to modification of electron distribution function by electric fields turns out to be inefficient in strong electric fields, although it describes current in weak electric fields. We further analyze the positions of maxima and minima of the differential resistance as a function of the applied electric field and frequency of microwave radiation.