Hole maximum density droplets of an antidot in strong magnetic fields

TL;DR

This paper studies the ground states and spin transitions of quantum antidots in the integer quantum Hall regime, revealing how shape and interactions influence their properties and matching experimental data.

Contribution

It introduces a Hartree-Fock approach combined with an electron-hole transformation to analyze antidot ground states and transitions, highlighting shape effects.

Findings

Maximum density hole droplets occur in certain parameter ranges.

Shape of the antidot significantly affects its physical properties.

Results align with capacitive interaction models and experimental observations.

Abstract

We investigate a quantum antidot in the integer quantum Hall regime (the filling factor is two) by using a Hartree-Fock approach and by transforming the electron antidot into a system which confines holes via an electron-hole transformation. We find that its ground state is the maximum density droplet of holes in certain parameter ranges. The competition between electron-electron interactions and the confinement potential governs the properties of the hole droplet such as its spin configuration. The ground-state transitions between the droplets with different spin configurations occur as magnetic field varies. For a bell-shape antidot containing about 300 holes, the features of the transitions are in good agreement with the predictions of a recently proposed capacitive interaction model for antidots as well as recent experimental observations. We show this agreement by obtaining the parameters of the capacitive interaction model from the Hartree-Fock results. An inverse parabolic antidot is also studied. Its ground-state transitions, however, display different magnetic-field dependence from that of a bell-shape antidot. Our study demonstrates that the shape of antidot potential affects its physical properties significantly.