Where are the edge-states near the quantum point contacts? A self-consistent approach

TL;DR

This paper presents a self-consistent method to analyze the distribution of edge states near quantum point contacts, emphasizing the impact of Coulomb interactions on current confinement and transport properties.

Contribution

It introduces a combined approach using Thomas-Fermi screening and local Ohm's law to accurately model electron-electron interactions and current distribution near QPCs.

Findings

Electron-electron interactions significantly alter edge state positions.

Current is confined within incompressible strips near QPCs.

Inclusion of Coulomb effects changes transport behavior predictions.

Abstract

In this work, we calculate the current distribution, in the close vicinity of the quantum point contacts (QPCs), taking into account the Coulomb interaction. In the first step, we calculate the bare confinement potential of a generic QPC and, in the presence of a perpendicular magnetic field, obtain the positions of the incompressible edge states (IES) taking into account electron-electron interaction within the Thomas-Fermi theory of screening. Using a local version of the Ohm's law, together with a relevant conductivity model, we also calculate the current distribution. We observe that, the imposed external current is confined locally into the incompressible strips. Our calculations demonstrate that, the inclusion of the electron-electron interaction, strongly changes the general picture of the transport through the QPCs.