Vortex formation in quantum dots in high magnetic fields

TL;DR

This paper investigates vortex formation in two-dimensional quantum dots under high magnetic fields using DFT and ED, revealing vortex entry at specific angular momenta and comparing the effectiveness of these methods.

Contribution

It provides a detailed comparison of DFT and ED in modeling vortex formation and highlights the limitations of DFT in high magnetic field regimes.

Findings

Vortices enter quantum dots one-by-one at specific angular momenta.

DFT results show good agreement with ED in predicting vortex states.

Vortices are observed both inside and outside the high-density regions.

Abstract

We study electronic structures of two-dimensional quantum dots in high magnetic fields using the density-functional theory (DFT) and the exact diagonalization (ED). With increasing magnetic field, beyond the formation of the totally spin-polarized maximum density droplet (MDD) state, the DFT gives the ground-state total angular momentum as a continuous function with well-defined plateaus. The plateaus agree well with the magic angular momenta of the ED calculation. By constructing a conditional wave function from the Kohn-Sham states we show that vortices enter the quantum dot one-by-one at the transition to the state with the adjacent magic angular momentum. Vortices are also observed outside the high-density region of the quantum dot. These findings are compared to the ED results and we report a significant agreement. We study also interpretations and limitations of the density functional approach in these calculations.