Interpretation of experiments implying density of states between Landau levels of a two-dimensional electron gas by a statistical model for inhomogeneities

A statistical model is presented for a spatially inhomogeneous two-dimensional electron gas in a quantizing magnetic field, which simulates the effect of Poisson’s equation and some essential properties of self-consistent screening. The model yields an effective background density of states between Landau levels and is used to explain a number of recent experimental observations. A three-dimensional model of a heterojunction is introduced, which can account for the possible charge transfer between the gate and the two-dimensional electron gas. We show that for GaAs heterostructures the variation of the depletion length as a function of the magnetic field may be neglected.