MAGNETOCAPACITANCE INVESTIGATION OF QUANTUM HALL-EFFECT AND EDGE STATES

The quantum Hall effect for the GaAs/AlGaAs heterostrcture is investig ated by an ac capacitance measurement between the two-dimensional elec tron system (2DES) and the gate on GaAs/AlGaAs. The capacitance minima at the quantum Hall plateaus are mainly determined not by the ODES ar ea under the gate but by the edge length of 2DES. There exists the hig h conductive region due to the edge states along the 2DES boundary, wh en the bulk conductivity sigma(xx) is small enough at low temperatures and high magnetic fields. From the temperature and frequency dependen ce of the capacitance minima, it is found that the measured capacitanc e consists of the contribution from the edge states and that of the bu lk state, which is treated as a distributed circuit of a resistive pla te with the conductivity sigma(xx). The evaluated width of edge states from the capacitance is much larger than the magnetic length and the cyclotron radius expected from the one-electron picture. This wide wid th of edge states can be explained by the compressible-incompressible strip model, in which the screening effect is taken into account. Furt her the bulk conductivity of less than 10(-12) S (S = 1/Omega) is meas ured by the capacitance of the Corbino geometry sample, where the edge states are absent and the capacitance is determined by only sigma(xx) in this geometry. The localization of the bulk state is investigated by the obtained sigma(xx).