We present a density-functional theory ͑DFT͒ approach to the study of the phase diagram of the maximumdensity droplet ͑MDD͒ in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level ͑LLL͒ approximation, analytical expressions are derived for the values of the parameters N ͑number of electrons͒ and B ͑magnetic field͒ 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 ͑HF͒ 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.
͓S0163-1829͑97͒06443-6͔Two-dimensional quantum dot systems, at high magnetic fields, have been recently studied by various authors. 1 The theoretical interest in these systems arises largely from the fact that they provide a few-electron realization of physical states that, in the macroscopic limit, are responsible for the occurrence of the quantum Hall effect. 2 The simplest example of such a state is the so-called maximum-density droplet ͑MDD͒, which, in the limit of a high magnetic field, can be written as a Slater determinant of lowest Landau level ͑LLL͒ orbitals with angular momenta 0,1, . . . ,NϪ1, where N is the number of electrons. 3 In the limit of N→ϱ this coincides with the incompressible state of the quantum Hall effect at filling factor ϭ1. Because, within the LLL, the MDD is the only N-electron state of angular momentum N(NϪ1)/2 ͑and there is none with lower angular momentum͒ it follows that it must be an exact eigenstate of the Hamiltonianif the small Coulomb coupling between different Landau levels is neglected. Here 0 is the frequency of the external parabolic potential, A i is the external vector potential, k is the dielectric constant, m* is the electron effective mass, B is the Bohr magneton, g* is the effective g factor for the Zeeman splitting, and i is the spin component along the axis perpendicular to the plane of the electrons. The question is whether this exact eigenstate ͑or rather its continuation to a finite magnetic field͒ can actually be the ground state of the quantum dot in some range of magnetic fields. The basic physics is simple: If the magnetic field is too large, the MDD cannot be the ground state because the compact arrangement of the electrons costs too much electrostatic energy. The electrostatic stress is released through a rearrangement of the electrons leading to a state of higher angular momentum. If, on the other hand, the magnetic field is too weak, the confinement energy will cause the external electrons in the MDD to be transferred to the center of the quantum dot, even though, in so doing, a higher Landau level becomes populated at the center of the dot. The conclusion of these arguments is that there will exist, at most, a ''window'' of magneti...
