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

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 phase diagram, which is in better agreement with the experimental results and the result of exact diagonalizations in the LLL than the HF calculations.