Density functional theory of the phase diagram of maximum density droplets in two-dimensional quantum dots in a magnetic field

TL;DR

This paper develops a density-functional theory approach to map the phase diagram of maximum density droplets in 2D quantum dots under magnetic fields, comparing results with other methods to understand edge reconstruction.

Contribution

It introduces a DFT method for analyzing phase transitions in quantum dots and compares its predictions with Kohn-Sham and Hartree-Fock calculations.

Findings

DFT predicts a more compact reconstructed edge than Hartree-Fock.

Analytical expressions for phase transition points are derived within the LLL approximation.

Results align closely with exact diagonalizations, validating the DFT approach.

Abstract

We present a density-functional theory (DFT) approach to the study of the phase diagram of the maximum density droplet (MDD) in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level (LLL) approximation, analytical expressions are derived for the values of the parameters $N$ (number of electrons) and $B$ (magnetic field) at which the transition from the MDD to a ``reconstructed'' phase takes place. The results are then compared with those of full Kohn-Sham calculations, giving thus information about both correlation and Landau level mixing effects. Our results are also contrasted with those of Hartree-Fock (HF) calculations, showing that DFT predicts a more compact reconstructed edge, which is closer to the result of exact diagonalizations in the LLL.