Hartree Treatment of Electron-Electron Interaction in the Integral Quantum Hall Effect. Screening Properties, Charge and Current Distribution

A quasi one-dimensional model for the charge and current distribution in the integral quantum Hall effect (QHE) is presented. The electron-electron interaction is included in the Hartree approximation. Temperature, sample size, applied Hall voltage and external fields may be varied over a wide range. Although the model does not include localization effects, it yields a distinct Hall plateau. Furthermore, it suggests a simple mechanism for the experimentally observed spatial current distribution behaviour.