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

TL;DR

This paper models the current and charge distribution in a 2D electron system to explain the origin of quantized Hall plateaus, emphasizing the role of incompressible strips and non-linear screening effects.

Contribution

It introduces a quasi-local transport model including non-linear screening and non-local conductivity effects to explain quantized Hall plateaus.

Findings

Quantized Hall plateaus correspond to the existence of incompressible strips.

The model reproduces finite width of plateaus and exact quantization of Hall resistance.

Potential variation differs significantly within and between 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.