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The microwave-induced resistance oscillations (MIRO) [1, 2] and the related zero-resistance states (ZRS) [3, 4] are novel phenomena in ultraclean two-dimensional electron system (2DES). In fact, there are still important puzzles in this research area.

We report our direct study of the compressibility on ultrahigh mobility two-dimensional electron system (μ ∼ 1 × 107 cm²/V sec) 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 [5] 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.

References
[1] M. A. Zudov, R. R. Du, J. A. Simmons, and J. L. Reno, Phys. Rev. B 64, 201311(R) (2001).
[2] P. D. Ye, L. W. Engel, D. C. Tsui, J. A. Simmons, J. R. Wendt, G. A. Vawter, and J. L. Reno, Appl. Phys. Lett. 79, 2193 (2001).
[3] R. G. Mani, Jurgen H. Smet, Klaus von Klitzing, Venkatesh Narayanamurti, William B. Johnson, and Vladimir Umansky, Nature 420, 646 (2002).
[4] M. A. Zudov, R. R. Du, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 90, 046807 (2003).
[5] A. V. Andreev, I. L. Aleiner, and A. J. Millis, Phys. Rev. Lett. 91, 056803 (2003).                                    

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