Electrostatic theory for imaging experiments on local charges in quantum Hall systems

TL;DR

This paper develops an electrostatic model for quantum Hall experiments, explaining how local charges and quasiparticles influence the system's electrostatic potential and charge states, providing a quantitative analysis framework.

Contribution

It introduces a simple electrostatic approach treating localized states as quantum dots within quantum Hall systems, enabling quantitative interpretation of experimental charge observations.

Findings

Electrostatic potential varies with local charge in quantum Hall systems.

Charge transition points are quantitatively predicted by the model.

Framework aids in analyzing experiments involving quasiparticle charging.

Abstract

We use a simple electrostatic treatment to model recent experiments on quantum Hall systems, in which charging of localised states by addition of integer or fractionally-charged quasiparticles is observed. Treating the localised state as a compressible quantum dot or antidot embedded in an incompressible background, we calculate the electrostatic potential in its vicinity as a function of its charge, and the chemical potential values at which its charge changes. The results offer a quantitative framework for analysis of the observations.