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.
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