Wigner molecules in quantum dots

Abstract

We perform unrestricted Hartree-Fock (HF) calculations for electrons in a parabolic quantum dot at zero magnetic field. The crossover from Fermi liquid to Wigner molecule behavior is studied for up to eight electrons and various spin components $S_z$. We compare the results with numerically exact path-integral Monte Carlo simulations and earlier HF studies. Even in the strongly correlated regime the symmetry breaking HF solutions provide accurate estimates for the energies and describe the one-particle densities qualitatively. However, the HF approximation favors the formation of a Wigner molecule and produces azimuthal modulations of the density for even numbers of electrons in one spatial shell.

5 pages, figures included