Electrostatics of the two-dimensional electron gas in a strong magnetic field

The properties of a two-dimensional electron liquid (2DEL) subjected to an external potential in a strong magnetic field are investigated. Two types of external potential are considered, random and periodic. A theory for nonlinear screening is developed, which assumes perfect screening in metallic regions. The results of computer modeling based on this nonlinear screening theory are in good agreement with recent magnetocapacitance data on the negative thermodynamic density of states (TDS) at integer filling factors. This theory also gives an explanation of the open-quotes backgroundclose quotes density of states as obtained from the activation energy of the conductivity, at integer filling factors, by von Klitzing's group. For a periodic antidot lattice, we have shown that the redistribution of electron density caused by a magnetic field shifts the plateaus of the transverse resistivity toward lower magnetic field. The position and width of the plateaus are in good agreement with experimental data. For a dot lattice it was shown that the shift of the plateaus should be in the opposite direction