Magnetocapacitance and the edge state of a two-dimensional electron system in the quantum Hall regime

The magnetic field dependence of the capacitance of a GaAs/AlGaAs heterostructure through a two-dimensional electron system (2DES) is measured in the quantum Hall regime. It is found that the values of the capacitance minima at the Hall plateaus are determined not by the 2DES area under the gate but by the edge length of the 2DES. These results cannot be explained by an existing interpretation of the magnetocapacitance, where the capacitance is directly related to the density of states of the 2DES. We suggest an alternative model in which the bottom values are essentially determined by the current carrying area at the edge. The widths of the current channels are estimated and compared with the recent theoretical and experimental estimates.