Distribution of an Ohmic current in the close vicinity of a quantum point contact

TL;DR

This paper investigates how an external current distributes in the vicinity of a quantum point contact within the quantum Hall regime, revealing that current is confined to incompressible regions with finite drift velocity, influenced by electron interactions.

Contribution

It provides a self-consistent theoretical analysis of current distribution near a QPC considering electron interactions and screening effects in the IQHE regime.

Findings

Current is confined to incompressible regions near the QPC.

Electron interactions lead to the formation of compressible and incompressible regions.

Distribution of incompressible strips influences quantum Hall plateau behavior.

Abstract

We present the essential findings of the screening theory of the integer quantum Hall effect (IQHE) considering a quantum point contact (QPC). Our approach is to solve the Poisson and the Schroedinger equations self-consistently, taking into account electron interactions, within a Hartree type approximation for a two dimensional electron gas (2DEG) subject to high perpendicular magnetic fields. The Coulomb interaction between the electrons separates 2DEG into two co-existing regions, namely quasi-metallic compressible and quasi-insulating incompressible regions, which exhibit peculiar screening and transport properties. In the presence of an external current, we show that this current is confined into the incompressible regions where the drift velocity is finite. In particular, we investigate the distribution of these incompressible strips and their relation with the quantum Hall plateaus considering a quasi 1D constriction, i.e. a QPC.