Screening model of metallic non-ideal contacts at integer quantized Hall regime

TL;DR

This paper presents a self-consistent model of electron and current density distributions in a 2D electron system under quantum Hall conditions, highlighting the effects of non-ideal contacts and heating on incompressible strip formation and transport.

Contribution

It introduces a comprehensive numerical model that accounts for non-ideal contacts, electron interactions, and heating effects, providing new insights into edge and bulk transport in quantum Hall systems.

Findings

Incompressible strips can be located at edges or bulk depending on magnetic field strength.

Non-ideal contacts prevent incompressible strips from reaching injection regions.

The model aligns with local probe experiments and explains hot-spot formation.

Abstract

In this work, we calculate the electron and the current density distributions both at the edges and the bulk of a two dimensional electron system, focusing on ideal and non-ideal contacts. A three dimensional Poisson equation is solved self-consistently to obtain the potential profile in the absence of an external magnetic field considering a Hall bar defined both by gates (contacts) and etching (lateral confinement). In the presence of a perpendicular magnetic field, we obtain the spatial distribution of the incompressible strips, taking into account the electron-electron interactions within the Thomas-Fermi approximation. Using a local version of Ohm's law, together with a relevant conductivity model, we also calculate the current distribution. We observe that the incompressible strips can reside either on the edge or at the bulk depending on the field strength. Our numerical results show that, due to a density poor region just in front of the contacts, the incompressible strips do not penetrate to the injection region when considering non-ideal contact configuration. Such a non-ideal contact is in strong contrast with the conventional edge channel pictures, hence has a strong influence on transport. We also take into account heating effects in a phenomenological manner and propose a current injection mechanism from the compressible regions to the incompressible regions. The model presented here perfectly agrees with the local probe experiments all together with the formation of hot-spots.