Structural properties of electrons in quantum dots in high magnetic fields: Crystalline character of cusp states and excitation spectra

The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These states are of crystalline character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66, 115315 (2002)]. The crystalline arrangement consists of concentric polygonal rings that rotate independently of each other, with the electrons on each ring rotating coherently. We show that the rotation stabilizes the Wigner molecule relative to the static one defined by the broken-symmetry unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the rotating Wigner molecule and pertinent features of the excitation spectrum, including the occurrence of a gap between the ground and first excited states that underlies the incompressibility of the system. This leads us to conjecture that the rotating crystal (and not the static one) remains the relevant ground state for low fractional fillings even at the thermodynamic limit.Comment: Published version. Typos corrected. REVTEX4. 10 pages with 8 postscript figures (5 in color). For related papers, see http://www.prism.gatech.edu/~ph274cy

Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons.Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy

Strongly correlated wave functions for artificial atoms and molecules

A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of total spin and angular momentum symmetries via Projection Techniques. Illustrative applications are presented for the case of a two-electron helium-like single quantum dot and a hydrogen-like quantum dot molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with extensive clarifications. A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers, see http://www.prism.gatech.edu/~ph274c