Constantine Yannouleas

Landau damping and wall dissipation in large metal clusters

Abstract In analogy with nuclear many-body studies, the discrete-matrix random phase approximation (RPA) is used to describe the photoabsorption of large, spherical metal clusters. In this limit, the single-peak, classical Mie regime is valid and the matrix-RPA equations can be solved analytically. The RPA yields a closed formula for the width, Γ, of this peak due to Landau damping. This width is inversely proportional to the radius R of the cluster, in agreement with experimental observations for large silver and gold clusters embedded in a host medium. The RPA proportionality coefficient is unequivocally determined, and the reasons for the uncertainty in its value arising from disagreements among previous theoretical approaches are discussed. Specifically, Γ = λg( h Ω sp e F ) v R , where λ is the multipolarity of the plasma vibration, Ω sp is the frequency of the surface plasmon, and eF is the Fermi energy of the conduction electrons. The function g varies from unity to zero as the frequency of the surface plasmon increases from zero to infinity. It is shown that the frequency dependence of g for a spherical shape is identical to that of a cubical boundary. v = ( 3v F 4 ){1 + ( π 2 6 )( T e F ) 2 } is the average speed of a Fermi gas at temperature T. This result indicates a very small dependence on temperature, a trend in agreement with the observation. A classical interpretation of this result is proposed based on the similarities with the onebody, wall-dissipation theory familiar from nuclear physics. According to this interpretation, the surface of the cluster is viewed as a moving wall whose interaction with the conduction electrons mimicks the multipole transitions induced by the electric field of the plasmon. This interpretation expresses Γ as the ratio, Γ = γ B , of a surface friction coefficient, γ, over an inertia mass, B. The 1 R dependence results from the fact that the inertia mass is proportional to the volume, whereas the friction coefficient is proportional to the surface of the cluster.

Stabilized-jellium description of neutral and multiply charged fullerenes Cx±60

Abstract A description of neutral and multiply charged fullerenes is proposed based on a stabilized jellium (structureless pseudopotential) approximation for the ionic background and the local density approximation for the σ and π valence electrons. A recently developed shell-correction method is used to calculate total energies and properties of both the neutral and multiply charged anionic and cationic fullerenes. The effect of the icosahedral symmetry is included perturbatively. The calculated single-particle energy level spectrum of C 60 is in good correspondence with experimentally measured ones and previous self-consistent local-density-approximation calculations. For the multiply charged fullerenes, we calculate microscopically the charging energies of C x ± 60 for up to x =12 excess charges. A semiclassical interpretation of these results is developed, which views the fullerenes as Coulomb islands possessing a classical capacitance. The calculated values for the first ionization potential and the first electron affinity agree well with the experimental ones. For the second and third ionization potentials, there exist substantial discrepancies in the experimental measurements. Our calculations support the results from charge transfer bracketing experiments and from direct ionization experiments through electron impact. The doubly charged negative ion is found to be very long-lived metastable species, in agreement with observations.

Symmetry breaking and quantum correlations in finite systems: studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semiconductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree?Fock level and of subsequent symmetry restoration via post Hartree?Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations.Strongly-correlated phenomena emerging from symmetry breaking include the following. Chemical bonding, dissociation and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot, with potential technological applications to solid-state quantum-computing devices. Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. Such electron molecules exhibit ro-vibrational excitation spectra, in analogy with natural molecules. At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches, offering a new point of view of the fractional quantum Hall regime in quantum dots (with possible implications for the thermodynamic limit). Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs). For a small number of bosons, the RBMs are energetically favored compared with the Gross?Pitaevskii solutions describing vortex formation. We discuss the present status concerning experimental signatures of such strongly correlated states, in view of the promising outlook created by the latest experimental improvements that are achieving unprecedented control over the range and strength of interparticle interactions.

Multiply Charged Metal Cluster Anions

Formation and stability patterns of silver dianionic and gold trianionic clusters are investigated with Penning-trap experiments and a shell-correction method including shape deformations. The theoretical predictions pertaining to the appearance sizes and electronic shell effects are in remarkable agreement with the experiments. Decay of the multiply anionic clusters occurs predominantly by electron tunneling through a Coulomb barrier rather than via fission, leading to appearance sizes unrelated to those of multiply cationic clusters.

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

Energetics and quantized conductance in jellium-modeled nanowires are investigated using the localdensity-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, or equivalently its minimum width, leads to the formation of self-selecting magic wire configurations, i.e., a discrete configurational sequence of enhanced stability, originating from quantization of the electronic spectrum, namely, formation of transverse subbands due to the reduced lateral dimensions of the wire. These subbands are the analogs of shells in finite-size, zero-dimensional fermionic systems, such as metal clusters, atomic nuclei, and 3 He clusters, where magic numbers are known to occur. These 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 2 e 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 most narrow part of the constriction in the wire. @S0163-1829~98!01908-0#

Structures and spectra of gold nanoclusters and quantum dot molecules

Abstract.Size-evolutions of structural and spectral properties in two types of finite systems are discussed. First we focus on energetics and structures of gold clusters, particularly AuN in the 40≲N≲200 range exhibiting a discrete sequence of optimal clusters with a decahedral structural motiff, and on the electronic structure of bare and methyl-thiol passivated Au38 clusters. Subsequently, bonding and spectra of quantum dot molecules (QDM’s) are investigated, using a single-particle two-center oscillator model and the local-spin-density (LSD) method, for a broad range of interdot distances and coupling strengths. A molecular orbital classification of the QDM states correlates between the united-dot and separated-dots limits. LSD addition energies and spin polarization patterns for QDM’s in the entire coupling range are analyzed, guiding the construction of a constant interaction model. A generalization of the non-interacting-electrons Darwin–Fock model to QDM’s is presented. Wigner crystallization of the electrons leading to formation of Wigner supermolecules is explored in both the field-free case and with a magnetic field using a spin-and-space unrestricted Hartree–Fock method.

Excitation Spectrum of Two Correlated Electrons in a Lateral Quantum Dot with Negligible Zeeman Splitting

The excitation spectrum of a two-electron quantum dot is investigated by tunneling spectroscopy in conjunction with theoretical calculations. The dot made from a material with negligible Zeeman splitting has a moderate spatial anisotropy leading to a splitting of the two lowest triplet states at zero magnetic field. In addition to the well-known triplet excitation at zero magnetic field, two additional excited states are found at finite magnetic field. The lower one is identified as the second excited singlet state on the basis of an avoided crossing with the first excited singlet state at finite fields. The measured spectra are in remarkable agreement with exact-diagonalization calculations. The results prove the significance of electron correlations and suggest the formation of a state with Wigner-molecular properties at low magnetic fields.

Multiply charged anionic metal clusters

Abstract The stability and decay channels of multiply charged anionic metal clusters are studied using the uniform jellium background model and the local density approximation, with self-interaction corrections when necessary. Shell effects are introduced using an adaptation of the nuclear Strutinsky method. Singly charged anions are stable for all sizes, but multiply charged negative ions are stable against spontaneous electron decay only above certain critical sizes. Below the border of stability, the anions are metastable against electron tunneling through a Coulombic barrier. Lifetimes for such decay processes are estimated. Fission channels may compete with the electron autodetachment and are studied for the case of doubly charged anions.

Electronic Entropy, Shell Structure, and Size-Evolutionary Patterns of Metal Clusters

We show that electronic-entropy effects in the size-evolutionary patterns of relatively small (as small as 20 atoms), simple-metal clusters already become prominent at moderate temperatures. Detailed agreement between our finite-temperature ‐ shell-correction-method calculations and experimental results is obtained for certain temperatures. This agreement includes a size-dependent smearing out of fine-structure features, accompanied by a measurable reduction of the heights of the steps marking major-shell and subshell closings, thus allowing for a quantitative analysis of cluster temperatures. [S0031-9007(97)02448-4] PACS numbers: 36.40. ‐ c Since the discovery [1] of electronic-shell-structure features in the abundance spectra of sodium clusters, similar features (the major ones corresponding to the degeneracies of a spherically symmetric mean-field potential [2,3]) have been routinely observed [4] in the size-evolutionary patterns (SEP’s) associated with other single-particle properties of both alkali- and noble-metal clusters. Specifically, such patterns pertain to ionization potentials (IP’s) [5‐ 7], electron affinities (EA’s) [8,9], monomer separation energies (MSE’s) [10], and fission dissociation energies [11]. It was early realized [12] that the secondary features in the mass spectra required the consideration of deformed cluster shapes [5,12]. When triaxial (ellipsoidal) shapes were considered in the framework of shell correction methods (SCM) [13‐ 16], substantial overall systematic agreement was achieved [14,15] between theory and experimental observations pertaining to the major and the fine structure of the aforementioned SEP’s. While deformation effects have been extensively studied, an understanding of the physical origins of thermal effects and their relation to the SEP’s is still lacking, even though the experiments are necessarily made with clusters at finite temperatures. Moreover, experimental determination of cluster temperatures remains a challenge, motivating the development of theoretical methods capable of extracting such information. While thermodynamic entropic contributions associated with the ionic degrees of freedom can be obtained from first-principles molecular-dynamics simulations [17,18], or from considerations of shape fluctuations in simpler models [19‐ 21], for sufficiently large simple-metal clusters MN with N . 20, the electronic entropy (which has not as yet been included in such studies) dominates the thermal characteristics of the shell structure, even at moderate temperatures. The prominent thermal effects associated with the electronic entropy are the focus of this paper. Without the simultaneous consideration of shape fluctuations, thermal effects pertaining to the electronic degrees of freedom and their relevance for the understanding of mass abundance spectra have been considered in the case of spherical neutral sodium clusters [22], and in a recent report [23] on the thermodynamics of neutral sodium clusters with axially symmetric shapes. In contrast to our findings, these studies have suggested that electronicentropy effects at moderate temperatures are not important for clusters with less than 100 atoms. The theoretical method used in this paper is a finitetemperature (F T) -SCM developed by us, which incorporates all three of the aforementioned aspects, namely, triaxial deformations, entropy of the electrons, and thermal effects originating from shape fluctuations. Furthermore, through a direct comparison with experimental measurements, we demonstrate that this method can be employed for determining cluster temperatures. Since the number of delocalized valence electrons is

Trial wave functions with long-range Coulomb correlations for two-dimensional N-electron systems in high magnetic fields

A new class of analytic wave functions is derived for two dimensional N-electron