Phase separation of edge states in the integer quantum Hall regime.

Coulomb effects on the edge states of a two-dimensional electron gas in the presence of a high magnetic field are studied for different widths of the boundaries. Schro\ifmmode\ddot\else\textasciidieresis\fi{}dinger and Poisson equations are self-consistently solved in the integer quantum Hall regime. Regions of flat bands at the Fermi level appear for smooth interfaces in order to minimize the electrostatic energy and are related to the existence of dipoles induced by the magnetic field. These plateaus determine the phase separation in stripes of compressible and incompressible electron liquids.