DENSITY OF STATES OF A 2-DIMENSIONAL ELECTRON-GAS IN A LONG-RANGE RANDOM POTENTIAL

The thermodynamic density of states and the density of states as obtained from the activation energy of the conductivity are calculated taking into account both linear and nonlinear electron screening. In the linear screening regime the density of states in a strong magnetic field is negative, and it is determined by electron-electron interaction. Linear screening fails when the filling factor is close to an integer. In the nonlinear screening regime the density of states is positive. The crossover between these regimes is shown to be verv sharp The quantitative results are obtained by computer modeling. They are in a good agreement with recent magnetocapacitance measurements and previous measurements of the activation energy in the regime of the quantum Hall effect.