Rotating quantum liquids crystallize

Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles.

Persistent Currents in Small, Imperfect Hubbard Rings

We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show, that the imperfection, whether localized or not, nearly always decrease, but can also \emph{increase} the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.

Metal Cluster — Surface Interaction: Simple Models and Ab Initio Calculations

We review recent ab initio atomistic calculations on interactions between metal clusters and electronically inert (insulating) substrates. The model system is sodium clusters on the sodium-chloride (001) surface. This system provides an example of weak cluster-support interaction (physisorption) which can however be easily modified by introducing color centers at the surface, resulting in chemisorption of sodium adatom or cluster. The results obtained from atomistic calculations can be used for constructing simple jellium-type models for the adsorbed cluster. These models allow for systematic investigations in a large size-range of clusters on the shell structure, dimensionality, and stabil…

Heat capacity of small superconducting disks

Abstract The superconducting state of small samples in a magnetic field is strongly dependent on the sample dimensions and geometry. We have initiated measurements of heat capacity of small superconducting disks. Our method, extensively used in many of our related experiments, is to measure the thermal time constant as a function of temperature of disks on a thin silicon nitride membrane. Theoretical results on heat capacity of the disks based on the Ginzburg–Landau theory will be presented.

Electronic-structure-induced deformations of liquid metal clusters

Ab initio molecular dynamics is used to study deformations of sodium clusters at temperatures $500\cdots 1100$ K. Open-shell Na$_{14}$ cluster has two shape isomers, prolate and oblate, in the liquid state. The deformation is stabilized by opening a gap at the Fermi level. The closed-shell Na$_8$ remains magic also at the liquid state.

Nuclear shell model applied to metallic clusters

We apply the nuclear shell model to jellium clusters of up to twenty-one Na atoms. Binding energies, ionization potentials, and photoabsorption cross sections are calculated and compared with mean-field results.

Metallic evolution of small magnesium clusters

Structural and electronic properties of small magnesium clusters (N≤13) are studied using a first-principles simulation method in conjunction with the density functional theory and generalized gradient correction approximation for the exchange-correlation energy functional. It is observed that the onset of metallization of magnesium clusters is hard to assign since both the s-p hybridization and the energy gap between the valence and conduction bands do not evolve rapidly towards the known bulk properties. Instead these quantities show a slow and nonmonotonic evolution.

Configuration-interaction calculations of jellium clusters by the nuclear shell model

Configuration-interaction (CI) calculations are performed on Na clusters of up to 20 atoms within the spherical jellium model, with particular attention paid to the magic clusters with N=2, 8, and 20. The interacting valence electrons are assumed to move in the Coulomb field of the jellium core. The numerical work is carried out by the nuclear-structure code oxbash modified to handle LS coupling. The many-particle bases are constructed of harmonic-oscillator single-particle states extending over 11 major shells and, alternatively, of single-particle states generated by the local-spin-density approximation (LSDA). The calculated quantities include ground- and excited state energies, ionizati…

Electronic polarizability of small sodium clusters.

Abstract : Small sodium clusters consisting of 1 to 40 atoms are described as spheres of interacting homogeneous electron gas (jellium model). The static electronic polarizability is calculated using self consistent density functional methods. An excellent agreement with recent experimental results is observed.

Behavior of the phonon gas in restricted geometries at low temperatures

Level-spacing distribution in the tight-binding model of fcc clusters.

A lattice-gas Monte Carlo method is used to simulate metallic fcc clusters at finite temperatures. A tight-binding model including s and p electrons has been derived for reproducing the free-electron-like energy band for the bulk metal and this model is used for calculating the electronic structures of the fcc cluster. The resulting level-spacing distribution at the Fermi energy is a Wigner distribution. The width of the distribution in small clusters is smaller than that calculated from the bulk density of states. In the lattice gas clusters the energy gaps related to the electronic magic numbers do not show up at the Fermi level. The energy between the last occupied and the first unoccupi…

Muon states in uniaxially strained iron

Effects of lattice relaxation, quantum motion, and uniaxial strain on the internal field at a positive-muon site in iron have been calculated. The uniaxial strain gives rise to a statistical shift of the muon population at interstitial sites. The effect of the population shift is found to be primarily responsible for the observed changes in the muon-precession frequency. The theory also predicts a 1T temperature dependence of the frequency shifts. Peer reviewed

The Kadanoff–Baym approach to double excitations in finite systems

We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are cha…

Unrestricted Shapes of Jellium Clusters

A jellium model with a completely relaxable background charge density is used to study metal clusters containing 2 to 22 electrons. The resulting shapes of the clusters exhibit breaking of axial and inversion symmetries, as well as molecular formation. The clusters without inversion symmetry are soft against deformation. The strongly deformed 14-electron cluster is found to be semi-magic. Stable-shape isomers are predicted.

On the shell structure and geometry of monovalent metal clusters

The Huckel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Huckel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Huckel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.

Energy spectrum, persistent current and electron localization in quantum rings

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body system can be described with a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the …

Models of Metal Clusters and Quantum Dots

The electronic structure of simple metal clusters and quantum dots is studied on the basis of the density functional theory and simple models. It is demonstrated that single-particle models explain well the gross features of deformation and magnetism in small clusters, nuclei and quantum dots and that the local density approximation can give valuable information of the internal structure of the manybody state.

Bright Beaches of Nanoscale Potassium Islands on Graphite in STM Imaging

We demonstrate, via scanning tunneling microscopy (STM) measurements performed at 48 K, the existence of "bright beaches" at the edges of K islands (diameter approximately 5-500 nm) on the graphite surface. The enhanced tunneling current is only observed in monolayer-high islands on graphite, and not in islands of similar geometry on top of a K monolayer film. First-principles density functional calculations and STM simulations suggest that this is an STM field effect, which appears as the positive tip attracts donated electrons back to the metallic K islands. The restored charge accumulates preferentially at the island edges.

Spontaneous magnetism of quantum dot lattices.

The magnetism of square lattices of quantum dots with up to 12 electrons per dot is studied using the spin-density functional formalism. At small values of the lattice constant, all lattices are nonmagnetic and gapless. When the lattice constant is increased, the shell structure of the single dots governs the magnetism of the lattice. At closed shells, the lattices are nonmagnetic and have a gap at the Fermi level. At the beginning and at the end of a shell, they become ferromagnetic and stay gapless up to large values of the lattice constant. Antiferromagnetism was observed only at midshell after a band gap was opened.

Current-spin-density-functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress t…

Magic triangular and tetrahedral clusters

Using the methods of density functional theory and the jellium model we show that clusters with triangular [in two dimensions (2D)] or tetrahedral [in three dimensions (3D)] shapes have a strong shell structure and enhanced stability. Moreover, the shell closings correspond to the lowest magic numbers of a 2D and 3D harmonic oscillator and at the same time to the number of divalent atoms in close-packed triangles and tetrahedrons. Ab initio molecular dynamics simulations for Na and Mg clusters support the results of the jellium model.

Finite boson and fermion systems under extreme rotation: edge reconstruction and vortex formation

Vortices can form when finite quantal systems are set rotating. In the limit of small particle numbers, the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. For a larger number of fermions, N greater than or similar to 15, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, as for example the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could, for instance, be electrons in a semiconductor heterostructure,…

Computer simulation of disordering and premelting of low-index faces of copper.

Molecular dynamics and the effective-medium theory have been applied to investigate the structure and dynamics of (110), (100), and (111) faces of copper in the whole temperature range from 0 K up to the bulk melting point, which has been determined to be 1240\ifmmode\pm\else\textpm\fi{}25 K. The observed order in the surface stability follows the order in the packing density. (110) disorders first via anharmonic effects (up to 700 K), then by vacancy-adatom formation and finally by premelting of the surface at about 1200 K. The (110) solid-melt interface is anisotropic and broadened, having a tendency to form small fluctuating (111) facets in equilibrium, which is suggested to be the atomi…

Fractional Periodicity of Persistent Currents: A Signature of Broken Internal Symmetry

We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin Hamiltonian holds the explanation to this transition. Numerical diagonalizations are performed to show this explicitely. Persistent currents therefore, provide an easy way to experimentally verify broken internal symmetry in electronic systems.

Linear Nuclei: A Density Functional Interpretation

We show that linear shape isomers of small even-even nuclei exist with nearly any internucleon interactions. The shapes of the linear isomers look like chains of alpha-particles, but single-particle spectrum reveals that alpha-particle interpretation is not needed. Indeed, the same shapes are obtained even with noninteracting particles in a rectangular cavity. Linear shape isomers are shown to exist also in metal clusters.

Ferromagnetism in small clusters.

Magnetization of small ferromagnetic clusters at finite temperatures has been studied using the Ising model and Monte Carlo techniques. The magnetization of finite clusters is reduced from the bulk value, and increases with the external magnetic field and with the cluster size. The results explain qualitatively the recent observations by de Heer, Milani, and Chatelain of the reduction with decreasing cluster size of the average magnetic moment in small iron clusters.

Electronic and magnetic structure of artificial atoms

The concept of shell structure has been found useful in the description of semiconductor quantum dots, which today can be made so small that they contain less than 20 electrons. We review the experimental discovery of magic numbers and spin alignment following Hund’s rules in the addition spectra of vertical quantum dots, and show that these results compare well to model calculations within spin density functional theory. We further discuss the occurrence of spin density waves in quantum dots and quantum wires. For deformable two-dimensional quantum dots (for example, jellium clusters on surfaces), we study the interplay between Hund’s rules and Jahn–Teller deformations and investigate the …

Atoms embedded in an electron gas: Immersion energies

Energies of atoms, H through Ar, embedded in a homogeneous electron gas are calculated within the density-functional scheme as a function of the electron-gas density. The energy-versus-density curves and the induced densities of states are analyzed and discussed in terms of the interaction properties of an atom with its environment. The low-density limit of the immersion energy is related to the electron-atom scattering length. The results should prove useful in detailed investigations of the recently suggested "quasiatom" or "effective-medium" approaches to chemical binding. The lowest-order estimates of the binding energies of diatomic molecules and chemisorbed atoms are obtained. Peer re…

Ionization potential of Al6 and Al7 as a function of temperature

The temperature-depence of the ionization potential of Al6 and Al7 clusters is studied by using ab initio molecular dynamics. The threshold regions of theoretical photoionization efficiency curves are obtained from the calculated ionization potential distributions by integration and the determined ionization potentials are compared with the experimental ones. Two important effects, which complicate the determination of ionization potential from photoionization efficiency curves, are observed: the thermal tail effect and the isomerization. Also a link between the adiabatic ionization potential and the threshold of the photoionization efficiency curve is discussed. In the case of Al7, this of…

Rotational and vibrational spectra of quantum rings

One can confine the two-dimensional electron gas in semiconductor heterostructures electrostatically or by etching techniques such that a small electron island is formed. These man-made ``artificial atoms'' provide the experimental realization of a text-book example of many-particle physics: a finite number of quantum particles in a trap. Much effort was spent on making such "quantum dots" smaller and going from the mesoscopic to the quantum regime. Far-reaching analogies to the physics of atoms, nuclei or metal clusters were obvious from the very beginning: The concepts of shell structure and Hund's rules were found to apply -- just as in real atoms! In this Letter, we report the discovery…

Universality of Many-Body States in Rotating Bose and Fermi Systems

We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest Landau level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain composite-fermion construction. We employ the exact-diagonalization technique for finding the many-body states. The overlap between the transformed boson ground state and the true fermion ground state is calculated in order to measure the quality of the transformation. For very small and high angular momenta, the overlap is typically above 90%. For intermediate angular momenta, mixing between states complicates the picture and leads to small ground-state overlaps at s…

Electronic structure of triangular, hexagonal and round graphene flakes near the Fermi level

The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at the Fermi level, and few low-energy conduction electron states occur both in triangular and hexagon…

Electronic properties of single-walled carbon nanotubes inside cyclic supermolecules

Possible ways for manipulating carbon nanotubes (CNTs) with cyclic supermolecules are studied using density functional theory. Electronic structure calculations with structure optimizations have been performed for the (4,4) and (8,0) single-walled carbon nanotubes (SWNTs) complexed with crown ethers as well as for the (4,0) SWNT with beta-cyclodextrin. A slight polarization of charge in both the nanotube and the supermolecule is observed upon rotaxane complexation, but the interaction is mainly repulsive, and the systems stay 2.8-3.5 A apart. The supermolecule does not affect the electronic band structure of the nanotube significantly within such a configuration. The situation differs notic…

Effects of Crystal Field Splitting and Surface Faceting on the Electronic Shell Structure

The shell structure of the valence electrons is clearly observed in all alkali and noble metal clusters containing up to hundreds of atoms[1 – 4]. It is seen in the abundances of the clusters, in the ionization potential and in the polarizability. The shell structure of the valence electrons is closely related to the shell model of nuclei, but is simpler owing to the negligibly small spin-orbit interaction. The ability to produce all sizes of metal clusters has made the metal clusters a test ground for the super-shell structure[5].

Ionization potential of aluminum clusters

Structure, electronic structure, and ionization potential of aluminum clusters of 2–23 atoms are studied with a total energy method based on the density-functional theory. The calculated adiabatic ionization potentials agree remarkably well with the data from threshold photoionization measurements. The analysis of results gives insight into hybridization effects in the smallest clusters as well as reveals certain clusters that exhibit a clear jellium-type shell structure. An explanation of the experimental results in the size region of 12–23 atoms is given in terms of coexisting, competing icosahedral, decahedral, and fcc-based clusters. @S0163-1829~98!00228-8#

Electronic polarizability of small metal spheres

We present the results of calculations for the ground-state electron structure, static polarizability, and dynamic response of small metal (jellium) spheres in vacuum or embedded in a dielectric. Fully self-consistent time-dependent density-functional methods are used. In particular, the static and dynamic responses to an incident electric field (dipolar polarizability and photoabsorption) are obtained. The results show substantial deviations from either classical or approximate quantum-mechanical solutions, and provide reference data for simplified treatments. Peer reviewed

Effect of melting on ionization potential of sodium clusters

The effect of melting transition on the ionization potential has been studied for sodium clusters with 40, 55, 142, and 147 atoms, using ab initio and classical molecular dynamics. Classical and ab initio simulations were performed to determine the ionization potential of Na142 and Na147 for solid, partly melted, and liquid structures. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster obtained with the ab initio method. However, in the case of 40 and 55 atom clusters, the ionization potential seems to decrease when the cluster melts.

Formation of Wigner molecules in small quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix.

Shell structure in large nonspherical metal clusters.

Electronic shell structure of icosahedral and cuboctahedral sodium clusters with 300 to 1500 atoms has been studied using a potential-well approximation for the effective one-electron potential. The results show that icosahedral clusters yield the same shell structure as spherical clusters up to the cluster size of about 500 atoms and that similarities persist until the cluster has about 1000 atoms. The shell structure of a cuboctahedral geometry begins to deviate from that of a sphere when the cluster size is about 100. A study on quadrupole deformations of large clusters shows that surface fluctuations in liquid clusters cannot destroy the shell structure even in the largest clusters.

Superparamagnetism in Ising Clusters

Recent experiments on small ferromagnetic clusters have inspired introduction of a number of seemingly quite different theoretical models. We shall argue that all these models show superparamagnetic behaviour above the blocking temperature but below the Curie temperature. In particular, we shall show that Ising clusters display superparamagnetism and introduce a simple correction to the usual tank behaviour of magnetisation which has to be included for very small clusters. We also discuss the dependence of magnetisation on coordination number.

Effects of the cluster surface on the electronic shell structure: faceting, roughness and softness

Several simple models have been used to study the effects of the surface on the electronic shell structure in metal clusters. The main results are as follows: The icosahedral clusters have the same electronic shell structure as the sphere up to about 1000 atoms. The surface roughness causes the distribution of the level spacings to be a Wigner distribution. By varying the softness of the potential we can obtain potentials where the simplest classical orbits are the ‘five-point star’ or even ‘the three-point star’.

Influence of electronic and geometric properties on melting of sodium clusters

Systematics of the melting transition for sodium clusters with 40-355 atoms has been studied with both ab initio and semiclassical molecular dynamics simulations. The melting temperatures obtained with an ab initio method for Na55 + and Na93 + correlate well with the experimental results. The semiclassically determined melting temperatures show similarities with the experimentally determined ones in the size region from 55 to 93 and near size 142, and the latent heat in the size region from 55 to 139, but not elsewhere in the size region studied. This indicates that the nonmonotonical melting behavior observed experimentally cannot be fully explained by geometrical effects. The semiclassica…

Aluminum cluster anions: Photoelectron spectroscopy andab initiosimulations

Atomic structures and geometries, electronic structure, and temperature-dependent photoelectron spectra of ${\mathrm{Al}}_{N}^{\ensuremath{-}} (N=19\ensuremath{-}102)$ clusters are studied both theoretically via ab initio local-density-functional simulations, and experimentally with high-resolution measurements. The use of a theoretically well-defined energy shift in conjunction with a generalized Koopmans' theorem enables direct comparisons between the calculated density of states and the experimental photoelectron spectrum. Such comparisons, using photoelectron spectra calculated for various relaxed cluster geometries, enables a determination of the optimal structures of the clusters. The…

Many-body origin of the plasmon resonance in small metal clusters

The origin of the plasmon excitation in small metal clusters is studied within the jellium model through ab initio electronic-structure calculations based on the nuclear shell model. In the limit of infinite size, the plasmon classically represents pure harmonic motion of the center of mass of the valence electrons. It is shown that this limit is already well approximated by clusters of only eight electrons.

Electronic Shell Structure and the Crystal Field Splitting in Simple Metals Clusters

An upper limit for the number of atoms in metal clusters capable of exhibiting electronic shell structure has been estimated by comparing the energy difference between the highest occupied and the lowest unoccupied state with the crystal field splitting. The former is obtained by solving the Schrodinger equation for a spherical potential well with hard walls while the latter is obtained from the band structure of the solid. The results indicate that shell structures may persist in clusters containing as many as a million atoms.

Unrestricted shapes of light nuclei in the local-density approximation: Comparison with jellium clusters

Abstract The shapes of light nuclei are studied within density-functional theory. The Kohn-Sham method and the local-density approximation are used. No symmetry restrictions are imposed. A parallel study is made of monovalent atomic clusters described on the jellium model. The shapes obtained for nuclei with Z = N = 2–22 show a striking similarity to those of atomic clusters of an equal number of valence electrons. Moments of inertia, when suitably normalized, are virtually identical. The calculated nuclear quadrupole moments are found insensitive to the effective interaction and in good agreement with experiment. Similar shape coexistence is established in both systems.

Aluminum-lithium clusters: First-principles simulation of geometries and electronic properties

The geometries and electronic properties of small lithium-rich ${\mathrm{Al}}_{N}{\mathrm{Li}}_{5N}$ $(N=1--6,10)$ clusters are studied using first-principles simulations. Aluminum ions form a compact inner core configuration in the clusters that changes into a chainlike skeleton embedded in a lithium surrounding as the cluster size increases. This behavior restricts $s\ensuremath{-}p$ hybridization effects and causes separate s and p bands in the electronic energy spectrum. A significant charge transfer from Li ions and nearby Al ions strengthens ionic Al-Li bonds, while Al-Al bonds gain a more covalent nature. The evolution of some bulk properties of $B2$ and $B32$ phases of AlLi alloys i…

Mie plasmon in polyhedral metal clusters

We study the dependence of the classical plasmon frequency on the symmetry of the metal cluster and show that all clusters with at least two three-fold axes have the same plasmon frequency as the spherical cluster, ωp/√3. In these cases the effect of the geometry will only appear in the spill-out correction and in other quantum mechanical corrections.

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.

Coreless Vortices in Rotating Two-Component Quantum Droplets

The rotation of a quantum liquid induces vortices to carry angular momentum. When the system is composed of multiple components that are distinguishable from each other, vortex cores in one component may be filled by particles of the other component, and coreless vortices form. Based on evidence from computational methods, here we show that the formation of coreless vortices occurs very similarly for repulsively interacting bosons and fermions, largely independent of the form of the particle interactions. We further address the connection to the Halperin wave functions of non-polarized quantum Hall states.

Vortex rings in two-dimensional harmonic traps

We use the configuration interaction technique to study vortex formation in rotating systems of interacting spinless fermions and bosons trapped in a two-dimensional harmonic potential. In the fermionic case, the vortices appear as holes in the Fermi sea and localize in rings. The yrast spectrum is dominated by rigid rotation of the vortex ring, showing periodic oscillations. The Bose system shows a similar yrast spectrum and vortex formation. This can be explained by a one-to-one correspondence of the fermion and boson many-particle configurations. A simple mean-field model can reproduce the oscillations in the yrast spectrum, but fails to explain the localization of vortices.

Properties of small antiferromagnetic Ising clusters

Magnetic properties of small antiferromagnetic clusters have been studied by using the Ising model with nearest-neighbour interactions. The number of atoms in the clusters varied between 6 and 30. Several cluster geometries were analysed in detail with the result that there is no generic phase diagram. In an external magnetic field magnetisation can increase with increasing temperature in a considerable temperature range. Magnetisation was found to strongly depend on both the overall geometry of the cluster and on the symmetry of the underlaying lattice structure.

DISORDERING MECHANISMS OF THE Cu(110) SURFACE

We review recent theoretical work on the various disordering mechanisms of the Cu(110) surface. In these studies the properties of the surface, from the onset of enhanced anharmonicity in surface vibrations up to bulk melting point T M , have been studied using molecular dynamics and lattice-gas Monte Carlo methods with many-body interactions derived from the effective medium theory. Well after the onset of enhanced out-of-plane surface vibrations, clustering of surface defects is found to induce a roughening transition at T≈0.81T M , and surface premelting is found to occur at T≈0.97T M . These results suggest, that these transitions can both appear at Cu(110). The general picture of diso…

Metal Clusters, Quantum Dots, and Trapped Atoms

In this chapter, we discuss the electronic structure of finite quantal systems on the nanoscale. After a few general remarks on the many-particle physics of the harmonic oscillator, likely being the most studied example for the many-body systems of finite quantal systems, we turn to the electronic structure of metal clusters. We discuss Jahn–Teller deformations for the so-called “ultimate” jellium model which assumes a complete cancelation of the electronic charge with the ionic background. Within this model, we are also able to understand the stable electronic shell structure of tetrahedral (three-dimensional) or triangular (two-dimensional [2D]) cluster geometries, resembling closed shell…

Edge-dependent selection rules in magic triangular graphene flakes

The electronic shell and supershell structure of triangular graphene quantum dots has been studied using density functional and tight-binding methods. The density functional calculations demonstrate that the electronic structure close to the Fermi energy is correctly described with a simple tight-binding model, where only the ${p}_{z}$ orbitals perpendicular to the graphene layer are included. The results show that (i) both at the bottom and at the top of the ${p}_{z}$ band, a supershell structure similar to that of free electrons confined in a triangular cavity is seen, (ii) close to the Fermi level, the shell structure is that of free massless particles, (iii) triangles with armchair edge…

Flat bands, Dirac cones, and atom dynamics in an optical lattice

We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or Hubbard models. In the case of fermions the release of the harmonic confinement removes fast atoms occupying the Dirac cones while those occupying the flat band remain immobile. Using exact diagonalization and dynamics we demonstrate that a similar strong occupation of the flat band does not happen in bosonic case and furthermore that the mean field model is not capable for describing the dynamics of the boson cloud.

Star orbits in metal clusters

A possibility that classical five-point star orbits play a dominant role for shell structures of large metal clusters is investigated quantum mechanically. With a soft Woods-Saxon spherical potential a signature of the five-point star orbit is found in the level densities. Quantum numbers of degenerate levels in the soft Woods-Saxon potential differ by 2 and 5 in radial nodes and angular momenta, respectively. Unlike the experimental observation the peaks in the mass spectrum are not equally spaced as a function of N 1/3 . The self-consistent jellium model does not reproduce the degeneracy associated with the five-point star orbits. It is demonstrated that by covering high-density metal clu…

Electron-hole duality and vortex rings in quantum dots

In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for rotating fermion condensates the vortices appear as holes in the Fermi see. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunnelling spectroscopy. We use the duality picture to show that these oscillations are caused by the localisation of vortices in rings.

Trapping of quasiparticles of a nonequilibrium superconductor

We have performed experiments where hot electrons are extracted from a normal metal into a superconductor through a tunnel junction. We have measured the cooling performance of such NIS junctions, especially in the cases where another normal metal electrode, a quasiparticle trap, is attached to the superconductor at different distances from the junction in direct metal-to-metal contact or through an oxide barrier. The direct contact at a submicron distance allows superior thermalization of the superconductor. We have analyzed theoretically the heat transport in this system. From both experiment and theory, it appears that NIS junctions can be used as refrigerators at low temperatures only w…

Photoionization of metal clusters.

The photoionization cross section of metal clusters is studied using simple theoretical models. In the case of small clusters, the plasmon is well below the photoionization threshold and the photoionization is dominated by simple independent-particle processes: One electron absorbs all the energy of the photon and immediately leaves the cluster. For large sodium clusters the photoionization efficiency curve is a result of a two-step process: First, the photon excites a plasmon and then the plasmon decays, either by emitting a photoelectron or by heating the cluster. A simple expression for the photoionization cross section near the threshold is derived. \textcopyright{} 1996 The American Ph…

Effects of the Surface and Finite Temperature on the Electronic Structure of Metal Clusters

The most fascinating feature of simple metal clusters is the existence of the electronic shell structure. This was observed first in alkali[1] and noble metals[2] and later also in some other nontransition metals[3,4,5]. The shell structure is a consequence of nearly free valence electrons confined to a finite volume. A spherical potential will always lead to a shell structure, the origin of which is the orbital angular momentum l and the large degeneracy (2l+1) associated with it. However, this primitive shell structure is strengthened by ’accidental’ degeneracies between states having different principal quantum numbers. Thus the shell structure of a hydrogen atom is different from that o…

Universal vortex formation in rotating traps with bosons and fermions.

When a system consisting of many interacting particles is set rotating, it may form vortices. This is familiar to us from every-day life: you can observe vortices while stirring your coffee or watching a hurricane. In the world of quantum mechanics, famous examples of vortices are superconducting films and rotating bosonic $^4$He or fermionic $^3$He liquids. Vortices are also observed in rotating Bose-Einstein condensates in atomic traps and are predicted to exist for paired fermionic atoms. Here we show that the rotation of trapped particles with a repulsive interaction leads to a similar vortex formation, regardless of whether the particles are bosons or (unpaired) fermions. The exact, qu…

Quantum dots in magnetic fields: Phase diagram and broken symmetry of the Chamon-Wen edge

Quantum dots in magnetic fields are studied within the current spin density functional formalism avoiding any spatial symmetry restrictions of the solutions. We find that the maximum density droplet reconstructs into states with broken internal symmetry: The Chamon-Wen edge co-exists with a modulation of the charge density along the edge. The phase boundaries between the polarization transition, the maximum density droplet and its reconstruction are in agreement with recent experimental results.

Interaction of two-level systems in amorphous materials with arbitrary phonon fields

To describe the interaction of the two level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this new model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a $6\times 6$ symmetric tensor of deformation potential parameters, $[R]$. Taking into account the isotropy of the amorphous solid, we deduce that $[R]$ has only two independent parameters. We show how these two parameters can be calculated from experimental data and we prove that for any amorphous bulk material the average coupling of TLSs with longitudinal phonons is always stronger than …

Quantum Motion of Chemisorbed Hydrogen on Ni Surfaces

Quantum mechanical energy levels and wave functions have been calculated for the motion of chemisorbed hydrogen atoms on Ni surfaces. The results show considerable quantum effects for the adatom in both the ground and the excited states. The description of the adparticles as being delocalized along the surface offers a novel interpretation of several phenomena, in particular the vibrational excitations. Peer reviewed

Close packing of clusters:  Application toAl100

The lowest energy configurations of close-packed clusters up to N=110 atoms with stacking faults are studied using the Monte Carlo method with Metropolis algorithm. Two types of contact interactions, a pair-potential and a many-atom interaction, are used. Enhanced stability is shown for N=12, 26, 38, 50, 59, 61, 68, 75, 79, 86, 100 and 102, of which only the sizes 38, 75, 79, 86, and 102 are pure FCC clusters, the others having stacking faults. A connection between the model potential and density functional calculations is studied in the case of Al_100. The density functional calculations are consistent with the experimental fact that there exist epitaxially grown FCC clusters starting from…

Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids

The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results are analyzed as a function of the total angular momentum of the system. Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5 etc. the system is fully polarized. The lowest energy states exhibit spin-waves, domains, and localization, depending on the angular momentum. Vortices exist only at excited polarized states. The high angular momentum limit shows localization of electrons and separation of the charge and spin excitations.

Electron-hole bilayer quantum dots: Phase diagram and exciton localization

We studied a vertical ``quantum dot molecule'', where one of the dots is occupied with electrons and the other with holes. We find that different phases occur in the ground state, depending on the carrier density and the interdot distance. When the system is dominated by shell structure, orbital degeneracies can be removed either by Hund's rule, or by Jahn-Teller deformation. Both mechanisms can lead to a maximum of the addition energy at mid-shell. At low densities and large interdot distances, bound electron-hole pairs are formed.

Many-body spectrum and particle localization in quantum dots and finite rotating Bose condensates

The yrast spectra (i.e. the lowest states for a given total angular momentum) of quantum dots in strong magnetic fields, are studied in terms of exact numerical diagonalization and analytic trial wave functions. We argue that certain features (cusps) in the many-body spectrum can be understood in terms of particle localization due to the strong field. A new class of trial wavefunctions supports the picture of the electrons being localized in Wigner molecule-like states consisting of consecutive rings of electrons, with low-lying excitations corresponding to rigid rotation of the outer ring of electrons. The geometry of the Wigner molecule is independent of interparticle interactions and the…

Sodium atoms and clusters on graphite by density functional theory

Sodium atoms and clusters $(Nl~5)$ on graphite (0001) are studied using density functional theory, pseudopotentials and periodic boundary conditions. A single Na atom is observed to bind at a hollow site 2.45 \AA{} above the surface with an adsorption energy of 0.51 eV. The small diffusion barrier of 0.06 eV indicates a flat potential energy surface. Increased Na coverage results in a weak adsorbate-substrate interaction, which is evident in the larger separation from the surface in the cases of ${\mathrm{Na}}_{3},$ ${\mathrm{Na}}_{4},$ ${\mathrm{Na}}_{5},$ and the $(2\ifmmode\times\else\texttimes\fi{}2)$ Na overlayer. The binding is weak for ${\mathrm{Na}}_{2},$ which has a full valence el…

Antiferromagnetic order and frustration in small clusters

Quantum rings for beginners II: Bosons versus fermions

The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in one-dimensional (1D) and quasi-one-dimensional (Q1D) quantum rings. In particular this involves comparing their many-body spectra and other properties, in various regimes and models, including spinless and spinful particles, finite versus infinite interaction, and continuum versus lattice models. Our aim is to present the topic in a comprehensive way, focusing on small systems where the many-body problem can be solved exactly. Mapping out the similarities a…

Density functional study of alkali-metal atoms and monolayers on graphite (0001)

Alkali metal atoms (Li, Na, K, Rb, Cs), dimers and (2$\times$2) monolayers on a graphite (0001) surface have been studied using density functional theory, pseudopotentials, and a periodic substrate. The adatoms bind at the hollow site (graphite hexagon), with Li lying closest to (1.84 ��) and Cs farthest (3.75 ��) from the surface. The adsorption energies range between $0.55-1.21$ eV, and the energy ordering of the alkali adatoms is Li$>$Cs$\ge$Rb$\ge$K$>$Na. The small diffusion barriers (0.02-0.21 eV for the C-C bridge) decrease as the atom size increases, indicating a flat potential energy surface. The formation (cohesion) energies of (2$\times$2) monolayers range between 0.55-0.81 …

Effects of preoperative group-based aquatic training on health related quality of life in persons with late stage knee osteoarthritis

drainage is better than resistance training alone as far as improvement in lymphedema is concerned. Implications: Lymphedema has a substantial effect on the upper limb functioning, independence as well as quality of life post mastectomy. Manual lymphatic drainage can help these patients to achieve functional independence and thereby increase their life quality in a simple, cost effective and efficient way.

Electronically induced trapping of hydrogen by impurities in niobium

The binding energies of hydrogen and its isotopes to substitutional impurities Ti, Cr, and V in niobium have been calculated. The hydrogen-metal interaction is based on the effective-medium theory. The wave mechanics of the hydrogenic interstitials are explicity dealt with, and the lattice distortion created by the hydrogen is incorporated through the method of lattice statics. The difference in the electronic structure between impurity and host atoms is shown to be largely responsible for the binding of hydrogen to the impurities. The results are in agreement with recent inelastic neutron scattering experiments. Peer reviewed

Screening of positrons in semiconductors and insulators

Theoretical models are presented for the enhancement of the electron density at a positron in a semiconductor or insulator host. The model better suited for typical semiconductors is based on the many-body theory for the screening of a positron in electron gas. The starting point of the model for insulators is the atomic polarizability. The common parameter in both models is the high-frequency dielectric constant. Moreover, the enhancement depends on the ambient electron density in the semiconductor model and on the unit-cell volume in the insulator model. With use of the models developed, positron lifetimes in perfect semiconductor and insulator crystals have been calculated. In the calcul…

Cu cluster shell structure at elevated temperatures

Equilibrium structures of small (3--29)-atom Cu clusters are determined by simulated annealing, and finite-temperature ensembles are simulated by Monte Carlo techniques using the effective-medium theory for the energy calculation. Clusters with 8, 18, and 20 atoms are found to be particularly stable. The equilibrium geometrical structures are determined and found to be determined by a Jahn-Teller distortion, which is found to affect the geometry also at high temperatures. The ``magic'' clusters retain their large stability even at elevated temperatures.

Spontaneous fragmentation of multiply charged metal clusters.

Tight-Binding Model for Spontaneous Magnetism of Quantum Dot Lattices

We use a simple tight-binding model to study the magnetism of two-dimensional quantum dot lattices with 1 to 12 electrons per dot. The results show that in the middle of an electron shell the lattice favours antiferromagnetism while with nearly empty or full shells ferromagnetism is favoured. The size of the antiferromagnetic region increases with the coordination number of the dot. A one-dimensional dot lattice shows a spin-Peierls transition. The results for a square lattice are in good agreement with density functional calculations of Koskinen et al.

Effects of preoperative aquatic resistance training on knee pain, mobility limitation and muscle impairments in people with late-stage knee osteoarthritis

Shell-model and projected mean-field approach to electronic excitations of atomic clusters

Electron-gas clusters: the ultimate jellium model

The local spin-density approximation is used to calculate ground- and isomeric-state geometries of jellium clusters with 2 to 22 electrons. The positive background charge of the model is completely deformable, both in shape and in density. The model has no input parameters. The resulting shapes of the clusters exhibit breaking of axial and inversion symmetries; in general the shapes are far from ellipsoidal. Those clusters which lack inversion symmetry are extremely soft against odd-multipole deformations. Some clusters can be interpreted as molecules built from magic clusters. The deformation produces a gap at the Fermi level. This results in a regular odd-even staggering of the total ener…

Density Functional Theory of Multicomponent Quantum Dots

Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different types of fermions with isotropic effective masses. The density functional method with the local density approximation is used. The increased number of internal (Kohn-Sham) states leads to a generalisation of Hund's first rule at high densities. At low densitites the formation of Wigner molecules is favored by the increased internal freedom.

Vortices in quantum droplets: Analogies between boson and fermion systems

The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions, in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum dots. When set to rotate, these in principle very different quantum systems show remarkable analogies. The topics reviewed include the structure of the finite rotating many-body state, universality of vortex formation and localization of vortices in both bosonic and fermionic systems, and the emergence of particle-vortex composites in the quantum Hall regime. An overview of the computational many-body techniques sets focus on the configuration interaction …

Roughening of the Cu(110) surface

The structure of the Cu(110) surface is studied at high temperatures using a combination of lattice-gas Monte Carlo and molecular dynamics methods with identical many-atom interactions derived from the effective medium theory. The anisotropic six-vertex model is used in the interpretation of the lattice-gas results. We find a clear roughening transition around T_R=1000K and T_R/T_M=0.81. Molecular dynamics reveals the clustering of surface defects as the atomistic mechanism of the transition and allows us to estimate characteristic time scales. For the system of size 50x50, the time scale of the local roughening at 1150 K of an initially smooth surface is of the order of 100 ps.

Properties of the Phonon Gas in Ultrathin Membranes at Low Temperature

We analyze heat conduction by phonons in ultrathin membranes by constructing a new theoreticalframework which implies a crossover from a bulk three-dimensional phonon distribution into a quasi-two-dimensional distribution when the temperature is lowered. We calculate the corresponding changesin the relevant thermodynamic quantities. At the end we make a comparison to experimental data.[S0031-9007(98)07273-1]

Hund's Rules and Spin Density Waves in Quantum Dots

Spin density functional theory is used to calculate the ground state electronic structures of circular parabolic quantum dots. We find that such dots either have a spin configuration determined by Hund's rule or make a spin-density-wave-like state with zero total spin. The dependence of the spin-density-wave amplitudes on the density of the two-dimensional electron gas is studied.

Magnetism in one-dimensional quantum dot arrays

We employ the density functional Kohn-Sham method in the local spin-density approximation to study the electronic structure and magnetism of quasi one-dimensional periodic arrays of few-electron quantum dots. At small values of the lattice constant, the single dots overlap, forming a non-magnetic quantum wire with nearly homogenous density. As the confinement perpendicular to the wire is increased, i.e. as the wire is squeezed to become more one-dimensional, it undergoes a spin-Peierls transition. Magnetism sets in as the quantum dots are placed further apart. It is determined by the electronic shell filling of the individual quantum dots. At larger values of the lattice constant, the band …

Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the $L$=0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As the field is increased the discontinuity slowly turns into a continuous change which is a finite size effect. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can …

Diffusion processes and growth on aluminum cluster surfaces

Diffusion processes of adatoms on icosahedral and Wulff polyhedral aluminum cluster surfaces have been studied by molecular dynamics simulations using the effective medium theory. Activation energies of diffusion mechanisms along {111} and {100} facets and from one facet to another, including different hopping and exchange processes as well as more exotic events, have been calculated. Exchange diffusion of an adatom by a chain mechanism through a {100} facet between two {111} facets and hopping diffusion across the edge between two {111} facets via a pull of another adatom on the neighbour facet are shown to play an important role. Adatoms on {111} facets are mobile already at very low temp…

Heating ofAl13−andAl14clusters

Dynamical properties of ${\mathrm{Al}}_{13}^{\ensuremath{-}}$ and ${\mathrm{Al}}_{14}$ clusters at a high-temperature regime are studied using a density functional theory based first-principles simulations method. During the heating ${\mathrm{Al}}_{13}^{\ensuremath{-}}$ shows a significantly different behavior than ${\mathrm{Al}}_{14}$ due to its double-magic nature. We also demonstrate that it is hard to assign any distinct melting transition for the studied cluster sizes. For ${\mathrm{Al}}_{13}^{\ensuremath{-}}$ we observe a solidlike behavior well after the melting temperature of bulk aluminum. In contradiction with the rare gas clusters we notice that the outermost atom of icosahedral …

Temperature Dependence of Irradiation-Induced Magnetic Flux Loss in Nd 2 Fe 14 B Permanent Magnets

Nd2Fe14B permanent magnets were irradiated with 20 MeV protons at 300 K and at 15 K, and the flux loss was measured as a function of the irradiation dose. The results show that at 15 K the Nd2Fe14B magnets can withstand particle radiation at least 1000 times more than at room temperature.

Jahn-Teller deformations of jellium slices

Equilibrium geometries of quasi two-dimensional jellium systems are calculated in the local density approximation, closely following the “Ultimate Jellium Model” of [1]. The background charge is assumed to be fully deformable in a layer between two parallel planes, whereas the wave functions in the direction perpendicular to such a “jellium slice” are confined to their ground state. Like for jellium clusters in three dimensions [1], we find that for various system sizes, a trend towards a breaking of axial and inversion symmetries is observable.

Vortices in rotating two-component boson and fermion traps

Quantum liquids may carry angular momentum by the formation of vortex states. This is well known for Bose-Einstein condensates in rotating traps, and was even found to occur in quantum dots at strong magnetic fields. Here we consider a two-component quantum liquid, where coreless vortices and interlaced lattices of coreless vortices appear in a very similar way for fermions and bosons with repulsive two-body interactions. The ground states at given angular momentum, as well as the pair correlations for equal and different numbers of atoms in the two components, are studied. (C) 2009 Elsevier B.V. All rights reserved.

Exchange-correlation energy of a multicomponent two-dimensional electron gas

We discuss the exchange-correlation energy of a multicomponent (multi-valley) two-dimensional electron gas and show that an extension of the recent parametrisation of the exchange-correlation energy by Attacalite et al (Phys. Rev. Lett. 88, 256601 (2002)) describes well also the multicomponent system. We suggest a simple mass dependence of the correlation energy and apply it to study the phase diagram of the multicomponent 2D electron (or hole) gas. The results show that even a small mass difference of the components (e.g. heavy and light holes) decreases the concentration of the lighter components already at relatively high densities.

Role of elastic and electronic interactions in trapping of hydrogen by impurities in transition metals

The interplay between the lattice distortion and the electronic contributions to the trapping of migrating hydrogen isotopes by substitutional impurities is investigated. We use a comprehensive calculational scheme incorporating (i) the effective-medium theory for the electronic interaction, (ii) the lattice Green’s function for elastic coupling, and (iii) the hydrogen quantum motion. The calculations for Ti and Cr impurities in V host show that lattice strain effects dominate. Cr, which otherwise provides an electronic trap site, does not induce trapping when elastic effects are incorporated. The situation in the case of Ti is just the reverse. We find no isotope dependence of the binding …

Magnetism and Hund's Rule in an Optical Lattice with Cold Fermions

Artificially confined, small quantum systems show a high potential for employing quantum physics in technology. Ultra-cold atom gases have opened an exciting laboratory in which to explore many-particle systems that are not accessible in conventional atomic or solid state physics. It appears promising that optical trapping of cold bosonic or fermionic atoms will make construction of devices with unprecedented precision possible in the future, thereby allowing experimenters to make their samples much more "clean", and hence more coherent. Trapped atomic quantum gases may thus provide an interesting alternative to the quantum dot nanostructures produced today. Optical lattices created by stan…

Photoelectron spectra of aluminum cluster anions: Temperature effects and ab initio simulations

Photoelectron (PES) spectra from aluminum cluster anions (from 12 to 15 atoms) at various temperature regimes, were studied using ab-initio molecular dynamics simulations and experimentally. The calculated PES spectra, obtained via shifting of the simulated electronic densities of states by the self-consistently determined values of the asymptotic exchange-correlation potential, agree well with the measured ones, allowing reliable structural assignments and theoretical estimation of the clusters' temperatures.

Thermal Expansion in Small Metal Clusters and its Impact on the Electric Polarizability

The thermal expansion coefficients of $\mathrm{Na}_{N}$ clusters with $8 \le N \le 40$ and $\mathrm{Al}_{7}$, $\mathrm{Al}_{13}^-$ and $\mathrm{Al}_{14}^-$ are obtained from {\it ab initio} Born-Oppenheimer LDA molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and size-dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. The polarizability is thus a sensitive indicator for thermal expansion. We …

Quantum Dots in Magnetic Fields: Phase Diagram and Broken Symmetry at the Maximum-Density-Droplet Edge

Quantum dots in magnetic fields are studied within the current spin-density-functional formalism avoiding any spatial symmetry restrictions of the solutions. We find that the maximum-density droplet reconstructs into states with broken internal symmetry: The Chamon-Wen edge coexists with a modulation of the charge density along the edge. The phase boundaries between the polarization transition, the maximum-density droplet, and its reconstruction are in agreement with recent experimental results.

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied by calculating the persistent current in small quantum rings and by exact simulations of the time evolution of the many-particle state in two cases: expansion of a localized cloud and collisions in a Newton’s cradle. We consider three different lattices which in the tight-binding model exhibit flat bands. The physical realization is considered to be an optical lattice with bosonic or fermionic atoms. The atoms are assumed to interact with a repulsive short-range interaction. The different statistics of bosons and fermions lead to different dynamics. Spinless fermions are easily trapped in the flat…

Comment on the Positron Surface-State Lifetime

Quand on calcule de facon coherente de l'energie de correlation des positons et la vitesse d'annihilation, la theorie explique au moins de facon qualitative la duree de vie de l'etat de surface des positons

Clusters-a New Source for Atomically Engineered Materials

ABSTRACTThe electronic structure and properties of small clusters are strongly dependent on their size. These size specific properties are illustrated by confining the discussion to three different topics (1) interaction of hydrogen with clusters (2) effect of temperature and magnetic field on the magnetization of clusters and (3) reaction of clusters with gas atoms. It is shown that the electronic energy levels that are strongly dependent on cluster size give rise to the size specific electronic properties of clusters. In cluster hydrides certain elements are found to absorb more hydrogen per atom in cluster form than in a crystalline form. The magnetization of clusters increases as a func…

Ellipsoidal deformation of vertical quantum dots

Addition energy spectra at 0 T of circular and ellipsoidally deformed few-electron vertical quantum dots are measured and compared to results of model calculations within spin-density functional theory. Because of the rotational symmetry of the lateral harmonic confining potential, circular dots show a pronounced shell structure. With the lifting of the single- particle level degeneracies, even a small deformation is found to radically alter the shell structure leading to significant modifications in the addition energy spectra. Breaking the circular symmetry with deformation also induces changes in the total spin. This "piezo-magnetic" behavior of quantum dots is discussed, and the additio…

Simulation of cluster impact fusion

We report molecular dynamics simulations of the impact of TiD clusters on TiD targets. In each cluster collision the total fusion probability seems to be due to a single deuterium deuterium collision. The kinetic energies of incident deuterium atoms gradually level off around the initial cluster energy, but do not reach the high energy tail of a corresponding Maxwell-Boltzmann distribution. Neither any other support for a thermonuclear fusion mechanism was observed. On the contrary, our simulations imply that the enhanced fusion rate is rather due to channeled many atom collision cascade type mechanism.

Ionization potential of Al6 and A17 as a function of temperature

The temperature-depence of the ionization potential of Al6 and Al7 clusters is studied by using ab initio molecular dynamics. The threshold regions of theoretical photoionization eciency curves are ob- tained from the calculated ionization potential distributions by integration and the determined ionization potentials are compared with the experimental ones. Two important eects, which complicate the determin- ation of ionization potential from photoionization eciency curves, are observed: the thermal tail eect and the isomerization. Also a link between the adiabatic ionization potential and the threshold of the photoion- ization eciency curve is discussed. In the case of Al7, this often use…

Large diamagnetic persistent currents

In multichannel rings, evanescent modes will always co-exist with propagating modes. The evanescent modes can carry a very large diamagnetic persistent current that can oscillate with energy and are very sensitive to impurity scattering. This provides a natural explanation for the large diamagnetic persistent currents observed in experiments.

Broken symmetries in the reconstruction of ν=1 quantum Hall edges

Spin-polarized reconstruction of the v=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon-Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern-Simons Ginzburg-Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region.

On the formation of Wigner molecules in small quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix.

Stacking faults in close-packed clusters

Ground state geometries of small hard sphere clusters were studied using two different type of contact interaction, a pair-potential and a many-atom interaction. Monte Carlo method in an FCC lattice with all possible (111) stacking faults was used to obtain the minimum energy geometries for clusters up to 59 atoms. Due to the surface energy, FCC packing is generally favoured as opposite to the HCP structure. However, in most cluster sizes the ground state obtained with the many-atom interaction has one or more stacking faults. The most symmetric geometry is usually not the ground state. Clusters with 59 and 100 atoms were studied due the possibility of a high symmetry cluster with stacking …

Phase coexistence in finite van der Waals systems

Phase coexistence in finite systems obeying van der Waals equation of state is studied by minimizing a model free energy function for a spherical liquid droplet and a gaseous phase around it. Phase diagrams are calculated for finite systems with a large range of sizes. According to this model, the highest temperature where a droplet and vapour can exist in equilibrium decreases as N −0.4, where N is the number of particles in the system. The model predicts higher equilibrium vapour pressures than molecular dynamics simulations.

Localization of particles in harmonic confinement: Effect of the interparticle interaction

We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation and vibrational modes of localized particles. We show that for a small number of particles the localization is similar for bosons and fermions. Moreover, independent of the range of the interaction the quantum mechanical spectrum at large angular momenta can be understood by vibrational modes of localized particles.

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring.

Metal clusters on an inert surface: A simple model

The shapes of metal clusters (with 2 to 14 valence electrons) on an inert surface are studied with a simple model based on the ultimate jellium model. It is shown that within certain approximations the surface-cluster interaction can be described with an external potential in the Kohn-Sham method. No restrictions for the cluster geometry are imposed. The results show that depending on the strength of the interaction and on the size of the cluster, the ground state is either planar or three-dimensional, but in many cases both geometries are stable and there is a marked energy barrier between them. The results agree qualitatively with ab initio calculations of Na clusters on a NaCl(100) surfa…

Correlation and spin polarization in quantum dots: Local spin density functional theory revisited

Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the …

Odd-even staggering in simple models of metal clusters

The odd-even staggering of free-electron metal clusters is studied using several simple models: Noninter-acting electrons in a rectangular box, triaxial harmonic oscillator, and Huckel model. Finite temperature effects are studied using the Monte Carlo method. All the models show qualitatively similar odd-even staggering. In the ground state the HOMO-LUMO gap is larger than the neighbouring energy gaps. The reduction of the odd-even staggering due to exchange and correlation is studied using the local-spin-density approximation.

Melting and multipole deformation of sodium clusters

Melting and multipole deformations of sodium clusters with up to 55 atoms are studied using an ab initio molecular dynamics method. The melting temperature regions for Na20, Na40, and Na 55 + are estimated. The melting temperature region determined here for Na 55 + agrees with the one determined experimentally. The dominating deformation type observed at the liquid phase for Na20 and Na40 is octupole deformation and for Na14 and Na 55 + quadrupole deformation.

Electronic Shell Structure in Icosahedral Metal Clusters

The shell structure of valence electrons in icosahedral and cuboctahedral simple metal clusters is studied using the free electron model and the Huckel model. The shell structure in a 1415 atom icosahedral cluster has still similarities with that of a spherical cluster. The effect of the finite temperature on the shell structure in liquid clusters is discussed.

Structural transitions and melting of copper clusters

Molecular dynamics is used to study the melting and structural transitions of small copper clusters. The melting temperature is found to be proportional to the average coordination number. Small icosahedral clusters melt at slightly higher temperatures than the cubic structures. Small cuboctahedral clusters are not stable but transform via a nondiffusive transition to icosahedral structure.

Interaction of Lamb modes with two-level systems in amorphous nanoscopic membranes

Using a generalized model of interaction between a two-level system (TLS) and an arbitrary deformation of the material, we calculate the interaction of Lamb modes with TLSs in amorphous nanoscopic membranes. We compare the mean free paths of the Lamb modes with different symmetries and calculate the heat conductivity $\kappa$. In the limit of an infinitely wide membrane, the heat conductivity is divergent. Nevertheless, the finite size of the membrane imposes a lower cut-off for the phonons frequencies, which leads to the temperature dependence $\kappa\propto T(a+b\ln T)$. This temperature dependence is a hallmark of the TLS-limited heat conductance at low temperature.

Electronic structure of quantum dots

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and…

Instability of cuboctahedral copper clusters.

Equilibrium structures of copper clusters up to 10 000 atoms are studied using molecular-dynamics and effective-medium theory. Icosahedral closed-shell clusters are most stable up to \ensuremath{\sim}2500 atoms and the Wulff polyhedra are favored for larger clusters. Cuboctahedral closed-shell clusters up to \ensuremath{\sim}2000 atoms are unstable. They undergo a nondiffusive transition to an icosahedral structure at low temperatures and melt directly above the fcc-cluster-melting temperature. The melting temperature decreases with decreasing cluster size but not as deeply as has been reported for pure metals.

Spin-density waves in superdeformed quantum dots

Abstract Electronic shell structure and spin effects in deformed quantum dots are investigated using spin-density functional theory. We recently suggested (Koskinen et al., Phys. Rev. Lett. 79 (1997) 1389) that for circular dots, depending on the density of the two-dimensional electron gas and the electron number, a spin-density wave-like state can occur as a possible ground state. Here these studies are extended to deformed and superdeformed dots, which approach the limit of a finite quantum wire.

A method for detecting vacancy diffusion in molecular dynamics

Diffusion on aluminum-cluster surfaces and the cluster growth

Diffusion of adatoms have been studied on fcc polyhedral aluminum-cluster surfaces by molecular-dynamics simulations using the effective-medium theory. Diffusion of adatoms has been shown to take place by hopping along ${111}$ facets at very low temperatures. Diffusion from one ${111}$ facet to other ${111}$ facets takes place at higher temperatures through a variety of mechanisms, and finally diffusion to and along ${100}$ facets takes place at high temperatures. Diffusion from ${100}$ to ${111}$ facets is possible only close to the melting temperature of the cluster. The appearance of different diffusion processes as a function of temperature is in good agreement with the calculated activ…

The tensor of interaction of a two-level system with an arbitrary strain field

The interaction between two-level systems (TLS) and strain fields in a solid is contained in the diagonal matrix element of the interaction hamiltonian, $\delta$, which, in general, has the expression $\delta=2[\gamma]:[S]$, with the tensor $[\gamma]$ describing the TLS ``deformability'' and $[S]$ being the symmetric strain tensor. We construct $[\gamma]$ on very general grounds, by associating to the TLS two objects: a direction, $\hat\bt$, and a forth rank tensor of coupling constants, $[[R]]$. Based on the method of construction and on the invariance of the expression of $\delta$ with respect to the symmetry transformation of the solid, we conclude that $[[R]]$ has the same structure as …

Electron correlation in metal clusters, quantum dots and quantum rings

This short review presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine stability and shape of the clusters. The ionic skeleton of alkali metals is soft, and cluster geometries are often solely determined by electron correlations. In quantum dots and rings, the electrons may be confined by an external electrostatic potential, formed by a gated heterostructure. In the low density limit, the electrons may form so-called Wigner molecules, for which the many-body quantum spectra reveal the classical vibration modes. High rotational states increase the tendency for the electrons to loca…

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state.

Quantum dots in magnetic fields: Unrestricted symmetries in the current spin-density functional formalism

We apply the current spin-density functional formalism (CSDFT) of Vignale and Rasolt to two-dimensional quantum dots in magnetic fields. Avoiding any spatial symmetry restrictions of the solutions, we find that a broken rotational symmetry of the electronic charge density can occur in high magnetic fields.

Vertical quantum dots with elliptically deformed cross sections

Abstract Few-electron vertical quantum dot artificial atoms with circular and elliptically deformed cross sections are investigated. Because of the high symmetry of the lateral confining potential, circular dots show a pronounced shell structure. With the lifting of level degeneracies, even a small deformation in shape is found to radically alter the shell structure leading to significant modifications of the addition energy spectra, and to induce change in the total spin.

S-matrix formulation of mesoscopic systems and evanescent modes.

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.

Shell structure and level spacing distribution in metallic clusters

The lattice gas Monte Carlo and tight binding method is used to study the electronic shell structure in large metallic clusters. The average density of states of a large ensemble of deformed clusters shows the same shell structure as the most spherical geometry. The level spacing distribution at the Fermi level is a Wigner distribution.

Deformations of quasi-two-dimensional electron gas clusters

Shell effects and Jahn-Teller deformations of quasi-two-dimensional jellium droplets are studied. Utilizing the ultimate jellium assumption, previously successfully used for three-dimensional systems, we calculate unrestricted shape relaxations and binding energies of the ground-state and the lowest isomers, using the methods of density-functional theory in the local spin-density approximation. Strong variations with particle number are found in the shape of the droplets. In particular, for certain magic electron numbers the shapes show triangular or circular symmetry, while for other electron numbers, more complicated symmetries are found. We finally show that from a more simple ``billiard…

Quantum rings for beginners: Energy spectra and persistent currents

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodic…

Quantum capacitance: a microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.

Core-melted clusters

The possibility of the existence of a core-melted cluster is investigated. To this end, a pair potential is introduced, with the property that the solid state of the cluster is less dense than the liquid state. With this kind of potential, the cluster exhibits a quite unusual behavior. In addition to the known states, solid, liquid, and surface-melted, it can also be found in a “dense-liquid” phase (a disordered state appearing at low temperatures), a “core-melted” phase, and a “core-surface-melted” phase. In the core-melted phase, the external part of the cluster consists of atoms that are vibrating around regular crystalline sites, while the core atoms have much bigger mobility, sometimes…