Symmetry breaking and Wigner molecules in few-electron quantum dots

We discuss symmetry breaking in two-dimensional quantum dots resulting from strong interelectron repulsion relative to the zero-point kinetic energy associated with the confining potential. Such symmetry breaking leads to the emergence of crystalline arrangements of electrons in the dot. The so-called Wigner molecules form already at field-free conditions. The appearance of rotating Wigner molecules in circular dots under high magnetic field, and their relation to magic angular momenta and quantum-Hall-effect fractional fillings, is also discussed. Recent calculations for two electrons in an elliptic quantum dot, using exact diagonalization and an approximate generalized-Heitler-London treatment, show that the electrons can localize and form a molecular dimer for screened interelectron repulsion. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements; its behavior reflects the effective dissociation of the dimer for large B. Knowledge of the dot shape and of J(B) allows determination of two measures of entanglement (concurrence and von Neumann entropy for indistinguishable fermions), whose behavior correlates also with the dissociation of the dimer. The theoretical value for the concurrence at B=0 agrees with the experimental estimates.Comment: LATEX, 12 pages with 6 figures. Invited talk at TNT2005 (Trends in Nanotechnology). To download a file with figures of higher quality, click http://www.prism.gatech.edu/~ph274cy/ (go to publication #74

Unified description of floppy and rigid rotating Wigner molecules formed in quantum dots

Restoration of broken circular symmetry is used to explore the characteristics of the ground states and the excitation spectra of rotating Wigner molecules (RWM's) formed in two-dimensional parabolic N-electron quantum dots. In high magnetic fields, the RWM's are floppy rotors with the energies of the magic angular momentum (L) states obeying aL + b/L^{1/2}. Under such fields the ground-state energies (referenced to the kinetic energy in the lowest Landau level) approach the electrostatic energy of N point charges in the classical equilibrium molecular configuration. At zero field and strong interelectron repulsion, the RWM's behave like quasiclassical rigid rotors whose energies vary as L^2. The particular L-dependence in high B is inherent and natural to a floppy rotating WM, and it can be used as a crucial diagnostic tool for resolving the recently posed question whether the composite-fermion or the RWM picture is appropriate for QD's.Comment: 5 pages. Revtex4 with 3 EPS figures and 2 tables . For related papers, see http://www.prism.gatech.edu/~ph274c

Microscopic description of the surface dipole plasmon in large Na_N clusters (950 < N < 12050)

Fully microscopic RPA/LDA calculations of the dipole plasmon for very large neutral and charged sodium clusters, Na_N^Z+, in the size range 950 < N < 12050 are presented for the first time. 60 different sizes are considered altogether, which allows for an in-depth investigation of the asymptotic behavior of both the width and the position of the plasmon.Comment: Latex/Revtex, 4 pages with 4 Postscript figures, accepted for publication in Physical Review

Coupling and Dissociation in Artificial Molecules

We show that the spin-and-space unrestricted Hartree-Fock method, in conjunction with the companion step of the restoration of spin and space symmetries via Projection Techniques (when such symmetries are broken), is able to describe the full range of couplings in two-dimensional double quantum dots, from the strong-coupling regime exhibiting delocalized molecular orbitals to the weak-coupling and dissociation regimes associated with a Generalized Valence Bond combination of atomic-type orbitals localized on the individual dots. The weak-coupling regime is always accompanied by an antiferromagnetic ordering of the spins of the individual dots. The cases of dihydrogen (H$_2$, $2e$) and dilithium (Li$_2$, $6e$) quantum dot molecules are discussed in detail.Comment: 7 pages. Latex with 4 GIF and 1 EPS figures. Based on an invited talk at the ISSPIC10 conference (see http://www.physics.gatech.edu/isspic10/) A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qds_isspic10.html For related papers, see http://www.prism.gatech.edu/~ph274c

Comment on "Density functional theory study of some structural and energetic properties of small lithium clusters" [J. Chem. Phys. 105, 9933 (1996)]

The Ionization Potentials of small Li_N clusters are calculated with a Shell Correction Method. They are used to illustrate that, within the jellium approximation, deformed cluster shapes provide an adequate description of the observed systematic size dependence of the properties of simple metal clusters. Such deformation effects were overlooked in the analysis of Gardet et al.Comment: Latex/Revtex, 2 pages with 1 Postscript figur