The spin-split incompressible edge states within empirical Hartree approximation at intermediately large Hall samples

TL;DR

This paper presents a self-consistent calculation method to analyze spin-resolved incompressible edge states in quantum Hall systems, incorporating exchange effects via an empirical g factor, and relates these states to longitudinal resistance behavior.

Contribution

It introduces a novel self-consistent Thomas-Fermi-Poisson scheme with empirical exchange effects to study spin-split edge states in quantum Hall samples.

Findings

Spin-resolved incompressible strips are successfully modeled.

The relation between edge states and longitudinal resistance is explicitly demonstrated.

The model captures the behavior at filling factors one and two.

Abstract

A self-consistent Thomas-Fermi-Poisson based calculation scheme is used to achieve spin resolved incompressible strips (ISs). The effect of exchange and correlation is incorporated by an empirically induced g factor. A local version of the Ohm's law describes the imposed fixed current, where the discrepancies of this model are resolved by a relevant spatial averaging process. The longitudinal resistance is obtained as a function of the perpendicular (strong) magnetic field at filling factor one and two plateaus. Interrelation between the ISs and the longitudinal zeros is explicitly shown.