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

Quantum Suppression of the Rayleigh Instability in Nanowires

A linear stability analysis of metallic nanowires is performed in the free-electron model using quantum chaos techniques. It is found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires.Comment: 10 pages, 5 eps figures, updated and expanded, accepted for publication in "Nonlinearity

Energetics, forces, and quantized conductance in jellium modeled metallic nanowires

Energetics and quantized conductance in jellium modeled nanowires are investigated using the local density functional based shell correction method, extending our previous study of uniform in shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volume conserving, adiabatically shaped constriction leads to formation of self selecting magic wire configurations. The variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e^2/h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.Comment: Latex/Revtex, 11 pages with 5 Postscript figure

Instability driven fragmentation of nanoscale fractal islands

Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by the deposition conditions and cluster composition. Sharing common features with other materials' breakup phenomena, the fragmentation instability is governed by the length-to-width ratio of the fractal arms.Comment: 5 pages, 3 figures, Physical Review Letters in pres

Nanojets, Electrospray, and Ion Field Evaporation: Molecular Dynamics Simulations and Laboratory Experiments

The energetics, interfacial properties, instabilities, and fragmentation patterns of electrosprays made from formamide salt solutions are investigated in a mass spectrometric vacuum electrospray experiment and using molecular dynamics (MD) simulations. The electrospray source is operated in a Taylor cone-jet mode, with the nanojet that forms being characterized by high surface-normal electric field strengths in the vicinity of 1 V/nm. Mass-to-charge ratios were determined for both positive and negative currents sprayed from NaI−formamide solutions with solute−solvent mole ratios of 1:8.4 and 1:36.9, and from KI−formamide solutions with mole ratios of 1:41 and 1:83. The molecular dynamics simulations were conducted on isolated 10 nm NaI−formamide droplets at mole ratios of 1:8 and 1:16. The droplet was subjected to a uniform electric field with strengths ranging between 0.5 and 1.5 V/nm. Both the experiments and simulations demonstrate a mixed charge emission regime where field-induced desorption of solvated ions and charged droplets occurs. The macroscopic parameters, such as average mass-to-charge ratio and maximum surface-normal field strengths deduced from the simulations are found to be in good agreement with the experimental work and consistent with electrohydrodynamic theory of cone-jets. The observed mass spectrometric Na+ and I− solvated ion distributions are consistent with a thermal evaporation process, and are correctly reproduced by the simulation after incorporation of the different flight times and unimolecular ion dissociation rates in the analysis. Alignment of formamide dipoles and field-induced reorganization of the positive and negative ionic charges in the interfacial region are both found to contribute to the surface-normal field near the points of charge emission. In the simulations the majority of cluster ions are found to be emitted from the tip of the jet rather than from the neck region next to the Taylor cone. This finding is consistent with the experimental energy distributions of the solvated ions which demonstrate that indeed most ions are emitted closer to the jet region, that is, beyond the cone-neck region where ohmic losses occur. This observation is also consistent with continuum electrohydrodynamic predictions of cluster-ion evaporation at surface regions of high curvature and therefore maximum surface electric field strengths, which may be the cone-neck region, the breakup region of the jet (usually near the tip of the jet), or the emitted charged droplets. In the nanoscale jets observed in this study, the regions of highest spatial curvature are at the ends of the jets where nascent drops either are forming or have just detached