Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus

Abstract

We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments.