Spatial structure of an incompressible Quantum Hall strip

Ivan A. Larkin†and L. S. Levitov‡ †Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK ‡Center for Materials Science & Engineering, Physics Department, MIT, Cambridge, MA-02139 Abstract The incompressible Quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic, indicating formation of a 1D Wigner crystal at the strip edge. Both effects, localized states and exchange, lead to a substantial increase of the strip width.