  To study the influence of microwave irradiation on two-dimensional electrons,
we apply a method based on capacitance measurements in GaAs quantum well
samples where the gate covers a central part of the layer. We find that the
capacitance oscillations at high magnetic fields, caused by the oscillations of
thermodynamic density of states, are not essentially modified by microwaves.
However, in the region of fields below 1 Tesla, we observe another set of
oscillation, with the period and the phase identical to those of microwave
induced resistance oscillations. The phenomenon of microwave induced
capacitance oscillations is explained in terms of violation of the Einstein
relation between conductivity and the diffusion coefficient in the presence of
microwaves, which leads to a dependence of the capacitor charging on the
anomalous conductivity. We also observe microwave-induced oscillations in the
capacitive response to periodic variations of external heating. These
oscillations appear due to the thermoelectric effect and are in antiphase with
microwave induced resistance oscillations because of the Corbino-like geometry
of our experimental setup.
