Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect

We report measurements and a self-consistent theory of the capacitance oscillations in a two-dimensional electron gas in the quantum-Hall-effect regime. The capacitance shows very strong structure which can be quantitatively explained as a function of temperature and frequency via the modulation of the conductivity of the inversion layer, without explicit reference to the density of states, except through the conductivity. When the Fermi level is in the localized portion of the density of states between the Landau levels (quantum Hall effect), the conductivity decreases rapidly and is difficult to measure; the capacitance signals, however, persist as the conductivity falls by many orders of magnitude. A new theoretical model of this resistive-capacitive, two-dimensional layer was developed which successfully accounts for the predominant features of the data and allows extraction of conductivity information from the capacitance measurements. Although previously the capacitance was thought to provide a mechanism for directly determining the density of states, this is shown not to be possible. Using the model to extract the conductivity, the temperature dependence of ${\sigma }_{\mathrm{xx}}$ was found to be activated, i.e., lnσ∼1/T, in agreement with other measurements. No appreciable frequency dependence of ${\sigma }_{\mathrm{xx}}$ was found over a two-decade range of frequency.