Screening of an impurity in a two-dimensional electron gas within the Hartree and the Hartree-Fock approximation in the quantum Hall regime

We investigate the static nonlinear screening of a single point charge (Coulombic impurity) by a two-dimensional electron gas (2DEG) in a strong perpendicular magnetic field at low temperature. The electron-electron interactions are treated in the Hartree-Fock approximation (HFA). The results are compared to earlier results for Hartree interacting electrons showing quite different screening properties due to the enhancement of the spin splitting of the Landau levels within the HFA. The possibility of different occupation of the spin levels of the impurity and the surrounding 2DEG is discussed in light of experiments.