Magnetocapacitance studies of two-dimensional electron systems with long-range potential fluctuations

We report on magnetocapacitance study of the quantum Hall effect (QHE) states. Capacitance minima width was found to be independent of magnetic field and to be the same for even, odd and fractional QHE states when measured as a function of the average electron density. This result indicates that the width of capacitance minima in the samples investigated are governed by long-range carrier density fluctuations. At low temperatures, the amplitudes of the minima decrease linearly with the temperature increase. All our experimental results for the integer QHE states are quantitatively explained by introducing unbroadened magnetic levels and dispersion of the electron density along the sample. The energy gaps at even filling factors obtained from fitting the experimental data are found to be close to the known cyclotron gaps. At odd fillings $\nu=1$, $3$ and $5$, the energy gaps appear to be enhanced in comparison with the Zeeman splitting, with the enhancement decreasing with filling factor.
The capacitance minima are argued to originate from the motion of incompressible regions along a sample caused by the gate voltage variation. We derive the condition for the appearance and motion of such regions for the case of gated samples with long-range fluctuations of density of charged donors.
The appearance of narrow magnetocapacitance peaks when a dc current is passed through the sample is reported. We hypothesize that these peaks are due to the current percolation along incompressible regions.