Vortex Clusters in Quantum Dots

TL;DR

This paper investigates vortex cluster formations in two-dimensional quantum dots under strong magnetic fields, revealing polygonal vortex arrangements through mean-field and exact methods, and discusses methodological differences.

Contribution

It introduces a new operator-based analysis for vortex structures and compares mean-field and exact solutions in quantum dot systems.

Findings

Vortex clusters form polygonal patterns inside quantum dots.

Mean-field and exact methods show similar vortex structures.

Differences and limitations of the methods are discussed.

Abstract

We study electronic structures of two-dimensional quantum dots in strong magnetic fields using mean-field density-functional theory and exact diagonalization. Our numerically accurate mean-field solutions show a reconstruction of the uniform-density electron droplet when the magnetic field flux quanta enter one by one the dot in stronger fields. These quanta correspond to repelling vortices forming polygonal clusters inside the dot. We find similar structures in the exact treatment of the problem using a new type of operator for the analysis. We discuss important differences and limitations of the methods used.