Density of states, screening and the width of the quantum Hall plateaus

We present a consistent treatment of the quantum Hall effect within the electrostatic approximation. We derive the form of the density of states (DOS) which differs from the usual gaussian shape valid for non-interacting electrons. Below a crossover temperature, this DOS gradually transforms into the non-interacting DOS near the Fermi energy. We obtain an estimate of this crossover temperature, which determines the range of validity of this framework, and allows a reconciliation of the width and temperature dependence of the quantum Hall plateaus with experiments. The DOS dramatically enhances the electron-lattice relaxation rate, thus reducing the possibility of electron overheating.