Self-consistent calculation of the electron distribution near a Quantum-Point Contact in the integer Quantum Hall Effect

TL;DR

This paper presents a self-consistent Thomas-Fermi-Poisson method to analyze electron distributions near a quantum point contact in the integer quantum Hall regime, revealing characteristic edge state rearrangements.

Contribution

It introduces a semi-analytical self-consistent approach to compute electrostatic potentials and electron densities in a 2DES with a QPC under magnetic fields.

Findings

Identification of three characteristic edge state rearrangements

Insights into current distribution near a QPC

Effect of temperature and magnetic field on electron density

Abstract

In this work we implement the self-consistent Thomas-Fermi-Poisson approach to a homogeneous two dimensional electron system (2DES). We compute the electrostatic potential produced inside a semiconductor structure by a quantum-point-contact (QPC) placed at the surface of the semiconductor and biased with appropriate voltages. The model is based on a semi-analytical solution of the Laplace equation. Starting from the calculated confining potential, the self-consistent (screened) potential and the electron densities are calculated for finite temperature and magnetic field. We observe that there are mainly three characteristic rearrangements of the incompressible "edge" states, which will determine the current distribution near a QPC.