Spontaneous symmetry breaking in single and molecular quantum dots

Classes of spontaneous symmetry breaking at zero and low magnetic fields in single quantum dots (QD's) and quantum dot molecules (QDM's) are discussed in relation to the ratio R_W between the interelectron Coulomb repulsion and the harmonic confinement, using spin-and-Space unrestricted Hartree-Fock calculations. These include: Wigner crystallization for R_W > 1, and formation of non-crystallized electron puddles localized on the individual dots in QDM's, as well as spin-density waves in single QD's, for R_W < 1. Erratum: Subsequent to the the publication of our Letter, we have performed further systematic spin-and-space unrestricted Hartree-Fock calculations. While the behavior and magnitudes of the addition energies shown in our Letter are maintained, as well as our finding pertaining to the prevalent violation of Hund's first rule, our improved calculations yield in certain instances different spin polarizations.