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 $R_W>1\mathrm{}$, and formation of noncrystallized electron puddles localized on the individual dots in QDM's, as well as spin-density waves in single QD's, for $R_W<1\mathrm{}$.