THE INTERRELATION BETWEEN INCOMPRESSIBLE STRIPS AND QUANTIZED HALL PLATEAUS

Abstract

We study the current and charge distribution of a two dimensional electron gas under strong perpendicular magnetic fields within the linear response regime. We show within a self-consistent screening theory that incompressible strips with integer values of local Landau-level filling factor exist for finite intervals of the magnetic field strength B. Within an essentially local conductivity model, we find that the current density in these B intervals is confined to the incompressible strips of vanishing local longitudinal resistivity. This leads to vanishing longitudinal and exactly quantized Hall resistance, and to a nice agreement of the calculated Hall potential profiles with the measured ones.