Quantum capacitance anomalies of two-dimensional non-equilibrium states under microwave irradiation

We report our direct study of the compressibility on ultrahigh mobility two-dimensional electron system ($\mu_{e} \sim 1 \times 10^{7}$ cm$^{2}$/Vs) in GaAs/AlGaAs quantum wells under microwave (MW) irradiation. The field penetration current results show that the quantum capacitance oscillates with microwave induced resistance oscillations (MIRO), however, the trend is opposite with respect to the compressibility for usual equilibrium states in previous theoretical explanations. The anomalous phenomena provide a platform for study on the non-equilibrium system under microwave, and point to the current domains and inhomogeneity induced by radiation. Moreover, the quantum capacitance indication for multi-photon process around $j = 1/2$ is detected under intensive microwave below 30 GHz.