Anticorrelation of compressibility and resistivity in a microwave-irradiated two-dimensional electron system

We report our direct study of the compressibility on an ultrahigh mobility two-dimensional electron system (${\ensuremath{\mu}}_{e}\ensuremath{\sim}$ $1\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$/V s) in GaAs/AlGaAs quantum wells under microwave irradiation. The field penetration current results show that the quantum capacitance oscillates with microwave-induced resistance oscillations, however, the trend is opposite with respect to the compressibility of equilibrium states in previous theoretical explanations. The anomalous phenomena provide a platform for study on the nonequilibrium system under microwaves. Moreover, the quantum capacitance indication for a multiphoton process around $j=1/2$ is detected under an intensive microwave below 30 GHz.