Finite Capacitive Response at the Quantum Hall Plateau

We study ultra-high-mobility two-dimensional (2D) electron/hole systems with high precision capacitance measurement. It is found that the capacitance charge appears only at the fringe of the gate at high magnetic field when the 2D conductivity decreases significantly. At integer quantum Hall effects, the capacitance vanishes and forms a plateau at high temperatures T\gtrsim 300 mK, which surprisingly disappears at T\lesssim 100 mK. This anomalous behavior is likely a manifestation that dilute particles/vacancies in the top-most Landau level form Wigner crystals, which have finite compressibility and can host polarization current.