Compressibility of a 2D electron gas under microwave radiation
  Microwave irradiation of a two-dimensional electron gas (2DEG) produces a non-equilibrium distribution of electrons, and leads to oscillations in the dissipative part of the conductivity. We show that the same non-equilibrium electron distribution induces strong oscillations in the 2DEG compressibility measured by local probes. Local measurements of the compressibility are expected to provide information about the domain structure of the zero resistance state of a 2DEG under microwave radiation. 
M.G. Vavilov, I.A. Dmitriev, I.L. Aleiner, A.D. Mirlin, and D.G.   Polyakov