Spin Ensemble Density Functional Theory for Inhomogeneous Quantum Hall Systems

TL;DR

This paper introduces a spin-inclusive ensemble density functional theory tailored for inhomogeneous quantum Hall systems, analyzing edge reconstruction phenomena in quantum dots under varying Zeeman splitting conditions.

Contribution

The work develops a novel spin-dependent ensemble DFT approach and applies it to study edge reconstruction in quantum dots, revealing polarization behaviors based on Zeeman splitting.

Findings

Edge reconstruction depends on Zeeman splitting

Polarized and unpolarized edge structures identified

Exchange hole formation at higher Zeeman splittings

Abstract

We have developed an ensemble density functional theory which includes spin degrees of freedom for nonuniform quantum Hall systems. We have applied this theory using a local-spin-density approximation to study the edge reconstruction of parabolically confined quantum dots. For a Zeeman splitting below a certain critical value, the edge of completely polarized maximum density droplet reconstructs into a spin-unpolarized structure. For larger Zeeman splittings, the edge remains polarized and develops an exchange hole.