Microwave-induced suppression of dissipative conductivity and its   Shubnikov -- de Haas oscillations in two-dimensional electron systems: Effect   of dynamic electron localization
  We present a model for microwave photoconductivity in two-dimensional electron systems (2DESs) in a magnetic field at the microwave frequencies lower that the electron cyclotron frequency when the intra-Landau level (LL) transitions dominate. Using this model, we explain the effect of decrease in the 2DES dissipative conductivity (and resistivity) and smearing of its Shubnikov -- de Haas oscillations by microwave radiation observed recently \cite{1,2}. The model invokes the concept of suppression of elastic impurity scattering of electrons by the microwave electric field. We calculated the dependence of the 2DES conductivity associated with intra-LL transitions as a function of the radiation and cyclotron frequencies and microwave power. The obtained dependences are consistent with the results of recent experimental observations \cite{1,2}. 
V. Ryzhii