Screening properties of the two-dimensional electron gas in the quantum Hall regime

The screening properties of a two-dimensional electron gas (2D EG) in a quantizing magnetic field at low temperatures are calculated within the Hartree approximation. The effect of a periodic external potential on the equilibrium state is studied for two models of the 2D EG, a strictly two-dimensional Hall strip geometry and a three-dimensional model of a heterostructure without lateral confinement. The single-particle energy spectrum is found to depend drastically on the collective state of the 2D EG, i.e., the position of the Fermi energy with respect to the Landau levels. Strong nonlinear effects, such as perfect screening in only a part of the sample and pinning of the energy spectrum to the Fermi level, are observed.