The Interrelation between Incompressible Strips and Quantized Hall Plateaus

TL;DR

This paper investigates how incompressible strips in a two-dimensional electron gas under strong magnetic fields relate to quantized Hall plateaus, showing that current confinement in these strips explains the quantization of Hall resistance.

Contribution

It demonstrates within a self-consistent screening theory that incompressible strips with integer Landau-level filling factors exist over finite magnetic field ranges and explains their role in quantized Hall effects.

Findings

Current density is confined to incompressible strips with vanishing longitudinal resistivity.

Hall resistance is exactly quantized in the presence of these strips.

Calculated Hall potential profiles agree with experimental measurements.

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.