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The non-physical effects on the transverse momentum transfer from fast electrons to gold nanoparticles associated to the use of non-causal dielectric functions are studied. A direct test of the causality based on the surface Kramers–Kronig relations is presented. This test is applied to the different dielectric function used to describe gold nanostructures in electron microscopy., A.R-C. acknowledges financial support from DGAPA/PAPIIT-UNAM project IA105917. R.E-S. acknowledges financial support from DGAPA/PAPIIT-UNAM project IN110916. N. Z. and A. R. acknowledge financial support from MINECO (FIS2016-80174-P) and Basque Government grant of UPV/EHU Grupos Consolidados IT-756-13.

Swift electron energy losses have been investigated in nanoporous alumina, taking into account retardation effects. A simple analytical expression is obtained for the energy loss probability. The electron energy loss spectra observed with the Scanning transmission electron microscope are reasonably well reproduced using a simple model consisting of a cylindrical shell of alumina surrounded by an effective porous medium. The Cherenkov radiation is responsible for energy losses below 8 eV. These losses are very sensitive to the shape of the nanostructures, up to distances much larger than the adiabatic length v/ω., Support from the Basque Government and the Basque Country University is gratefully acknowledged.

In the framework of the classical dielectric theory, the role of the image potential in electron energy loss spectroscopy (EELS) of fast electrons commonly used in scanning transmission electron microscopy travelling near a surface is studied. Relativistic and dispersive corrections are evaluated to establish the range of validity of this theory. The spatial resolution of the EELS technique is discussed for valence and core electron excitations. The effect of the quantal nature of the probe is also discussed. Finally, several problems involving planar surfaces, small particles, cylinders and truncated targets of interest in nanotechnology are studied., The authors thank the Basque Government for financial support (PI-1997-39).

The ground-state electronic structures of cylindrical quantum wires are studied within the stabilized jellium model and using the spin-dependent density-functional theory. The subband structure is shown to affect the cohesive properties, causing an oscillating structure in the force needed to elongate the wire. Because the steps in the quantized conductance reflect also the subband structure a correlation between the force oscillations and conductance steps is established. The model also predicts magnetic solutions commensurate with the subband structure and consequently additional steps in the conductance., N. Z. acknowledges the financial support of the Spanish Ministry of Education DGES, Project Reference PR95-591.

We study theoretically the quantum well states (QWSs) localized in Pb overlayers on Cu(111) surface. Particular emphasis is given to the states with energies close to the vacuum level. Inclusion of the long-range image potential tail into the model potential description of the system allows us to show the effect of hybridization between QWSs and image potential states (ISs). The particle-in-a-box energy sequence characteristic for QWSs evolves into the Rydberg series converging towards the vacuum level. The electron density of the corresponding states is partially moved from inside the metal overlayer into the vacuum. The decay rates due to the inelastic electron-electron scattering decrease with increasing energy, opposite to >conventional> QWSs and similar to the ISs. Many-body and wave packet propagation calculations of the inelastic decay rates are supplemented by simple analysis based on the phase accumulation model and wave-function penetration approximation. This allows an analytical description of the dependence of the QWS/ISs hybridization on different parameters and, in particular, on the overlayer thickness. © 2012 American Physical Society., This work was partially funded by MCINN(FIS2010-19609-C02-01) and G.V-UPV/EHU(IT- 366-07).

We present a theoretical study of the constant current scanning tunneling spectroscopy of quantum well states localized in Pb(111) overlayers on Cu(111) surfaces. The distance-voltage characteristic of the tunneling junction is obtained with a mixed approach. The wave packet propagation technique is applied to describe electron tunneling from the tip into the sample, and the density functional calculations provide the necessary inputs for the one-dimensional model potential representation of the system. The excited-state population decay mechanisms via inelastic electron-electron and electron-phonon interactions are taken into account with a bias-dependent absorbing potential introduced in the metal. Our results are in good agreement with recent experimental studies over the energy range where the free-electron description of the Pb overlayer used here applies. We find that at high bias the quantum well states experience a Stark energy shift and partially acquire a character of field emission resonances. The present model study also sheds light at the experimentally observed departure of the energies of the quantum well states from the particle-in-a-box prediction for the bias above 4 eV. The measured trend can be consistently explained as due to the departure of the realistic Pb band structure in the Γ-L direction from free-electron parabola when the electron momentum approaches the Γ point. © 2011 American Physical Society.

10 páginas, 6 figuras, 3 tablas.-- PACS number(s): 73.40.Jn, 73.23.Ad, 73.63.Nm, 73.63.Rt, We study the conductance during the elongation and breakage of Na nanowires described with the ultimate jellium model. A combined approach is used where the nanowire breakage is simulated self-consistently within the density-functional theory, and the wave packet propagation technique is applied for ballistic electron transport. For certain conditions the breakage of the nanowire is preceded by formation of clusters of magic size in the break junction. This affects the conductance G, in particular the shape of the G=3G0 to G=G0 (=2e2/h) step upon elongation. The observed trends can be explained as due to the transient trapping of ballistic electrons inside the cluster, leading to a resonant character of the electron transport through the break junction. The cluster-derived resonances appear as peak structures in the differential conductance which may serve as an experimental signature of clustering., This work has been funded partially by the University of theBasque Country UPV/EHU (Grant No.GIC07IT36607), the Departamento de Educación del Gobierno Vasco, and the Spanish Ministerio de Ciencia y Technología (MCyT) (Grant No. FIS2007-66711-C02-01). The SGI/IZO-SGIker UPV/EHU (supported by the National Program for the Promotion of Human Resources within the National Plan of Scientific Research, Development and Innovation - Fondo Social Europeo, MCyT and Basque Government) as well as the Academy of Finland through its Centers of Excellence Program are gratefully acknowledged.

1 página, 1 figura.-- PACS numbers: 68.37.Ef, 68.65.Fg, 73.21.Fg, This work was partially funded by MCINN(FIS2010- 19609-C02-01) and G.V-UPV/EHU(IT-366-07).

The optical properties of a nanoparticle dimer bridged by a conductive junction depend strongly on the junction conductivity. As the conductivity increases, the bonding dimer plasmon blueshifts and broadens. For large conductance, a low energy charge transfer plasmon also appears in the spectra with a line width that decreases with increasing conductance. A simple physical model for the understanding of the spectral feature is presented. Our finding of a strong influence of junction conductivity on the optical spectrum suggests that plasmonic cavities might serve as probes of molecular conductance at elevated frequencies not accessible through electrical measurements., This project was supported by the Robert A. Welch Foundation, Grants C-1220 and C-1222(P.N., N.J.H.), Etortek project inanoGUNE from the Basque Government (BG), Project FIS2007-066711-C02-00 from the Spanish MICINN, Grant IT-366-07 from BG-UPV/EHU and Project EUI2008-03816 CUBiHOLE from the internationalization national plan of the Spanish MICINN within the EU ERA-NET projects (J.A., N.Z., O.P.G.). Computational resources were provided by IZO-SGIker (UPV/EHU, MICINN, BG, ESF).

A standard many-body method, based on the spherical-harmonics representation of the Bethe-Salpeter ladder solution for the two-particle scattering amplitude in two-dimensional jellium electron gases, is applied to determine a pair formation temperature Tp from the pole of the pairing vertex. In this method, pairing may occur due to attractive spherical harmonics in the input interparticle interaction. The comparative study was performed with parametrized models for this interaction obtained by considering the real-space aspects of screening holes around moving electrons. The theoretical, maximal pair formation temperatures are in the ∼100K range and appear at small values of the density of the jellium system., The work of I.N. was supported partly by the Hungarian OTKA -Grant No. T049571 and that of N.Z. and P.M.E. by the University of Basque Country and the Basque Unibertsitate eta Ikerketa Saila GV-UPV/EHU s/n Grant No. IT-366-07 and the Spanish MCyT Grant No. FIS2007-66711-C02-01

If the bare interaction between two electrons is dressed in the two-dimensional (2D) electron gas by the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in cases where the basic dressing is described by superimposing normalized holes centered around both electrons. Beyond this modeling, a possible modification of the interaction energy at short range is considered by a repulsive potential term. The effect of the ionic polarizability on pair interaction is approximated by a static dielectric constant. A many-body analysis of pairing, employing the spherical harmonics representation of the Bethe–Salpeter ladder-solution for the two-particle scattering amplitude in 2D, is given as well. Pairing occurs due to attractive spherical harmonics in our interparticle potential., The work of IN has been supported partly by the Hungarian OTKA (Grant No. T049571), that of NZ and PME by the University of the Basque Country and the Basque Unibertsitate eta Ikerketa Saila (GV-UPV/EHU (s/n) IT-366-07) and the Spanish MCyT (FIS2007-66711-C02-01).

11 páginas, 8 figuras, 1 tabla.-- PACS number(s): 73.21.Fg, 73.50.Gr, 73.20.At, 78.47.-p.-- Trabajo presentado al "DIPC10 : Passion for Knowledge" celebrado en Donostia (España) del 27 de septiembre al 1 de octubre de 2010., We present results of calculations of the lifetimes of excited electrons (holes) in quantum well states and quantum well resonances in Pb overlayers supported on Cu(111). Many-body decay via inelastic energy relaxation and one-electron decay via energy-conserving one-electron transfer into the substrate are considered. One-electron energies and wave functions have been computed for different coverages of the Pb overlayer (from 1 to 18 monolayers) by using a one-dimensional pseudopotential for the entire overlayer-substrate system in the framework of density functional theory within the local density approximation. The elastic (energy-conserving resonant electron transfer) contribution to the total lifetime broadening of quantum well resonances has been calculated within the wave packet propagation method. The inelastic electron-electron (many-body) contribution to the lifetime broadening of both occupied and unoccupied quantum well states has been evaluated using GW approximation. The decay mechanisms of both quantum well states and quantum well resonances in thick overlayers are discussed., This work has been funded partially by the University of the Basque Country UPV/EHU (Grant No. GIC07IT36607), the Departamento de Educación del Gobierno Vasco, and the Spanish Ministerio de Ciencía y Technología (MCyT) (Grant No. FIS2007-66711-C02-01).

8 pages, 7 figures.-- Printed version published on Aug 6, 2008., The role of quantum well states (QWSs) and quantum well resonances (QWRs) in the stability of metallic overlayers is studied. When the substrate presents a confining gap, as it is the case of Cu(111), the stability is determined by QWSs and there is experimental evidence of the existence of magic thicknesses. For overlayers which do not have QWSs, as those grown on Al(111), we explore the existence of thicknesses of enhanced stability due to QWRs by comparing the strength of the oscillations in the surface energy., We acknowledge partial support by the University of the Basque Country and the Basque Hezkuntza Unibertsitate eta Ikerkuntza Saila (Grant No. IT-366-07), and Spanish MEC (FIS2007-65711-C02-01 and MAT2006-12743). The SGI/IZO-SGIker UPV/EHU (supported by the National Program for the Promotion of Human Resources within the National Plan of Scientific Research, Development and Innovation—Fondo Social Europeo, MCyT and Basque Government) is gratefully acknowledged for generous allocation of computational resources. This work was also partially supported by the Academy of Finland through its Centre of Excellence Program.

Electronic states of one monolayer high Na nanoislands on the Cu(111) surface are studied as a function of the nanoisland size. Properties of nanoislands such as one-electron states, the electron density, and the associated potential are obtained self-consistently within the density-functional formalism using a one-dimensional pseudopotential for the Cu(111) substrate and the jellium model for Na. A wave packet propagation method is used to study the energies and lifetimes of quasistationary states localized at Na islands. For very large islands, island-localized states merge into the two-dimensional continuum of the Na quantum well state. Thus, we assign the quasistationary states studied as arising from the quantization of the two-dimensional quantum well continuum due to the finite island size. The scattering at the island boundaries results in the energy-conserving resonant electron transfer into the continuum of the substrate states broadening the island-localized states into resonances.

Abnormally large stability of Pb nanostructures grown on metallic or semiconductor substrates has been observed even for heights of about 30 monolayers. Using both density-functional theory calculations and analytical models, we demonstrate that the stability at even higher coverages (N>30 ML) is supported by an extra second quantum beat pattern in the energetics of the metal film as a function of the number of atomic layers. This pattern is triggered by the butterflylike shape of the Fermi surface of lead in the (111) direction and supports the detection of stable magic islands of higher heights than measured up to now., This work was supported by the ETORTEK -NANOMAT program of the Basque government, Spanish Ministerio de Ciencia y Tecnología -MCyT of Spain -Grant No. Fis 2004-06490-CO3-00, the European Network of Excellence NANOQUANTA -NM4-CT-2004-500198 and the Intramural Special Project -Ref. 2006601242. The SGI/IZOSGIker UPV/EHU supported by the National Program for the Promotion of Human Resources within the National Plan of Scientific Research, Development and Innovation-Fondo Social Europeo, MCyT and Basque Government is gratefully acknowledged for allocation of computational resources.

If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated LixZrNCl superconductors., The work of I.N. has been supported partly by the Hungarian OTKA -Grants Nos. T046868 and T049571, that of M.J.P. by the Academy of Finland, and that of N.Z. by the University of Basque Country Grant No. 9/UPV00206.215-13639/2001, the Basque Unibertsitate eta Ikerketa Saila, the MCyT Grant No. FIS2004-06490-C03-00, and the EU Network of Excellence NANOQUANTA Grant No. NMP4-CT-2004-500198.

Our theoretical study shows how well-resolved image potential states develop on metal-supported metallic nanoislands. The systems under consideration are one monolayer high Na nanoislands on the Cu(111) surface. However, the phenomenon is general and it requires only that the work function of the adsorbate is lower than that of the substrate, and that the substrate possesses a projected band gap along the surface normal., This work has been supported by the University of the Basque Country, the Spanish Ministerio de Ciencia y Tecnología, the Academy of Finland through its Centers of Excellence project, and the Finnish Funding agency for Technology and Innovation.

We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has recently arisen in experiments on impurities on metal surfaces with Shockley surface states. Mathematical theorems ascertain a bound state for two-dimensional circularly symmetric potentials V(r) with ∫∞0drrV(r)⩽0. We find that a shielded potential with ∫∞0drrV(r)>0 may also sustain a bound state. Moreover, on the same footing we study the electron-electron interactions in the two-dimensional electron gas, finding a bound state with an energy minimum for a certain electron gas density., The work of I.N. has been supported partly by the Hungarian OTKA -Grants No. T046868 and No. T049571, that of M.J.P. by the Academy of Finland, and that of N.Z. by the University of Basque Country -Grant No. 9/UPV00206.215-13639/2001 and the Basque Unibertsitate eta Ikerketa Saila, the MCyT -Grant No. FIS2004-06490-C03-00, and the EU Network of Excellence NANOQUANTA -Grant No. NMP4-CT-2004-500198.

A method to determine the temperature of metallic amorphous alloys when heated with a current pulse (`flash annealing`) is proposed. With some energetical considerations we calculate the temperature of the sample during the fast heat treatment. Theoretical curves calculated in that way are in good agreement with experimental results. The temperature of the sample during the pulse is experimentally determined by measuring the spontaneous magnetization during the current heating and comparing this with the magnetization-temperature curve obtained when heating in a conventional furnace. The influence of the different parameters appearing in the mathematical expressions on the heating process, such as the characteristics of the material, the geometry of the ribbon or the annealing conditions, is also studied.

The appearance of “magic” heights of Pb islands grown on Cu(111) is studied by self-consistent electronic structure calculations. The Cu(111) substrate is modeled with a one-dimensional pseudopotential reproducing the essential features, i.e., the band gap and the work function, of the Cu band structure in the [111] direction. Pb islands are presented as stabilized jellium overlayers. The experimental eigenenergies of the quantum-well states confined in the Pb overlayer are well reproduced. The total energy oscillates as a continuous function of the overlayer thickness reflecting the electronic shell structure. The energies for completed Pb monolayers show a modulated oscillatory pattern reminiscent of the supershell structure of clusters and nanowires. The energy minima correlate remarkably well with the measured most probable heights of Pb islands. The proper modeling of the substrate is crucial to set the quantitative agreement., This work was partially supported by the University of the Basque Country (Grant No. UPV00224.310-14553/2002), Departamento de Educacion del Gobierno Vasco (Grant No. MAT 2001-0946), Spanish MCyT (Grants Nos. PB98-0870-C02 and MAT 2002-04087-C02-01), and by the Academy of Finland through its Centre of Excellence Program (2000-2005).

We present a method for density-functional modeling of metallic overlayers grown on a support. It offers a useful tool to study nanostructures, combining the power of self-consistent pseudopotential calculations with the simplicity of a one-dimensional approach. The model is illustrated for Pb layers grown on the Cu(111) surface. The analysis provides the strength of the electron confinement barriers in thin slabs with accuracy, supporting the interpretation of the quantum well state spectra measured by scanning tunneling spectroscopy. On the other hand, it offers a benchmark to check the simple analytical models commonly used in the literature to study metallic films on semiconducting or metallic surfaces. As a result, some deficiencies are detected in the applicability of those models, which often lead to an overestimation of the number of wetting layers. Finally, an improved formula is proposed., We acknowledge partial support by the University of the Basque Country s9/UPV00224.310-14553/2002d, the Basque Hezkuntza Unibertsitate eta Ikerkuntza Saila and the Spanish Ministerio de Ciencia y Tecnología MAT 2001-0946 and MAT2002-04087-CO2-O1d. This work was also partially supported by the Academy of Finland through its Centre of Excellence Program s2000–2005d and by the European Community sixth Framework Network of Excellence NANOQUANTA sNMP4-CT-2004-500198d.

The effect of dielectric boundaries on the Cherenkov radiation (CR) produced when a fast point charge moves inside or near a material is analyzed for different shapes of the sample. Calculations are offered for a charge moving near both planar and nonplanar surfaces. CR is found to be produced even when the external charge moves outside a semi-infinite medium. For charges moving near planar boundaries, the reflected radiation interferes with the direct CR, leading to oscillations in the emission probability as a function of the impact parameter relative to the interfaces. Thin-film guided modes are excited by penetrating electrons and our calculations agree reasonably well with available experiments. The bulk limit in the emission probability is recovered for charges passing by the center of cylinders or spheres of increasingly large radius. Recent experiments of energy loss of electrons passing near dielectric spheres are explained thanks to the inclusion of retardation effects in the sphere response. These effects lead to an efficient channel of radiative energy losses. Finally, the diffraction of CR in void inclusions is proposed as a tool for providing information on otherwise inaccessible buried structures., Help and support from the Basque Departamento de Educacion, Universidades e Investigacion, the University of the Basque Country UPV/EHU Contract No. 00206.215-13639/2001, and the Spanish Ministerio de Ciencia y Tecnologia Contract No. MAT2001-0946 is gratefully acknowledged.

We have predicted, using a cylindrical stabilized-jellium model and self-consistent electronic structure calculations within the local spin density approximation, that simple metal nanowires may exhibit spontaneous magnetization. Stable magnetic solutions occur for certain wire radii, at which the occupancy of the highest subband below the Fermi level is small. Thereafter, we have found by first-principles calculations that a linear chain of Al atoms becomes magnetic at interatomic distances large enough. The magnetic solution is conserved when the linear chain relaxes to form a zig-zag wire and even after adsorption on the NaCl(1 0 0) surface which is a mean to control the geometry of the atomic wire.

The excitations produced by fast electrons impinging perpendicularly on both metallic and semiconductor cylindrical nanowires are investigated within the framework of dielectric theory. The dependence of the electron energy-loss spectra (EELS) on the nanowire radius is studied in detail, and so is the spatial extension of the induced-charge fluctuations associated to the modes that are excited during the loss process. The limits of applicability of dielectric theory to nanowires are discussed. In particular, comparison between the present theory and EELS measurements performed with silicon nanofibers support the use of dielectric theory at the scale of a few nanometers in diameter, and it is shown that this positive result is justified in terms of the longitudinal pattern of the induced surface plasmons. Finally, the effect of nanowire termination on the electron energy-loss probability for electrons passing near the edge is calculated using the boundary charge method, showing that the range of this effect can extend up to tens of nanometers for low-energy m=0 modes., Support from the Basque government and Basque Country University is acknowledged. One of the authors E.O. also acknowledges the Spanish Ministerio de Educacion y Cultura for financial support under Contract No. PB98-0780-C02.

On the basis of self-consistent density-functional calculations, it is predicted that three-dimensional nanowires of simple (nonmagnetic) metals undergo a transition to a spin-polarized magnetic state at critical radii. The magnetic transition also contributes to the elongation force on the nanowire. The force exhibits oscillations due to quantum confinement, in tune with the conductance steps as the wire is pulled., N. Z. acknowledges support from the Spanish Ministry of Education (DGES), Project No. PR95-591, and the Laboratory of Physics of the HUT for the hospitality.

The stress and annealing dependence of the Curie temperature in FeZrBCu alloys is presented. A change of about 50°/GPa has been observed. The change in amorphous matrix composition upon crystallization produces an expected increase in TC (about 200°C) which is similar to the experimentally observed increase. This behaviour is opposite to that observed in Fe-Nb based alloys., This work was supported by the Spanish CICYT under grant MAT93-0691. Two of the authors (P.G. and I.O.) wish to thank the Basque Government for financial support under a FPI gran

In the frame of the self-energy formalism, the energy loss spectrum for STEM electrons moving close to a sphere coupled to a planar surface is studied. As an application the problem of the coupling between a small metallic particle and a large supporting surface is studied, as well as its dependence on both the size of the particle and the dielectric nature of the support. The coupling between both surfaces is found to be relevant only for particles of radius less than νω−1, where ω is the energy transfer and ν is the electron velocity. This result is explained in terms of the range of the Coulomb interaction. Our results are in qualitative agreement with recent experimental data., Authors gratefully thank help and support from Gipuzkoako Foru Aldundia and the Basque Country Government (PGV9114).

From a self-energy approach, a general expression for the energy loss probability in scanning transmission electron microscopy is derived. As an application, the coupling between a small particle and the supporting surface is studied.

Expressions for the energy loss due to interaction with surfaces experienced by fast electrons passing through holes drilled in a coated medium are derived within the framework of the classical dielectric theory. These expressions are evaluated for Al coated with alumina using experimental values of the dielectric constant ϵ(ω) of the different media. Retarded energy loss probabilities are derived and some applications are discussed. Deflection effects due to the image force acting on the particle are also analysed., The authors wish to thank Gipuzkoako Foru Aldundia, the Basque Country Government (Eusko Jaurlaritza) and the Spanish CAYIT for financial support.

We present a novel concept of a magnetically tunable plasmonic crystal based on the excitation of Fano lattice surface modes in periodic arrays of magnetic and optically anisotropic nanoantennas. We show how coherent diffractive far-field coupling between elliptical nickel nanoantennas is governed by the two in-plane, orthogonal and spectrally detuned plasmonic responses of the individual building block, one directly induced by the incident radiation and the other induced by the application of an external magnetic field. The consequent excitation of magnetic field-induced Fano lattice surface modes leads to highly tunable and amplified magneto-optical effects as compared to a continuous film or metasurfaces made of disordered noninteracting magnetoplasmonic anisotropic nanoantennas. The concepts presented here can be exploited to design novel magnetoplasmonic sensors based on coupled localized plasmonic resonances, and nanoscale metamaterials for precise control and magnetically driven tunability of light polarization states., N.M., M.P., and P.V. acknowledge support from Basque Government under the Project n. PI2015-1-19 and from MINECO under the Project FIS2015-64519-R. N.M. acknowledges support from the Predoctoral Program of the Basque Government through Grant PRE-2015-2-0113. M.P. acknowledges support from the Spanish Ministry of Economy and Competitiveness through Grant BES-2013-063690. M.P. thanks Dr. Luca Pietrobon for valuable inputs on fabrication process using Electron Beam Lithography. M.K. and S.v.D. acknowledge support from the National Programme in Nanoscience and the Academy of Finland (Grant 263510). L.B., M.K., S.N.Z., and J.A. acknowledge financial support from Project No. FIS2013-41184-P of MINECO, Project ETORTEK IE14-393 NANOGUNE’14 of the Department of Industry of the Government of the Basque Country, and support from the Basque Department of Education and the UPV-EHU (Grant IT-756-13).

The stability of sodium nanowires is studied by modeling them as infinite uniform jellium cylinders and solving self-consistently for the electronic structure. The total energy per unit length oscillates as a function of the wire radius giving a shell structure. The amplitude of the energy oscillations attenuates regularly, reflecting a supershell structure. We compare our theoretical results with recent experiments [A. I. Yanson et al., Nature 400, 144 (1999); Phys. Rev. Lett. 84, 5832 (2000)] performed by the mechanically controllable break junctions (MCB) technique. The comparison clarifies the origin of the observed shell structure and especially the formation of the quantum beats of the supershell structure and supports the conclusions based on an earlier semiclassical model. The comparison is also a quantitative test for the reliability of the simple stabilized-jellium model as well as for the accuracy of the equation used to relate the conductivity and the area of the narrowest point of the constriction.

We present here electron energy loss spectra (EELS) calculations for an infinite set of aligned dielectric spheres as a first approximation to calculations in a more complex periodic array with small computer cost. The boundary charge method is analytically developed for such a system with use of local dielectric theory. A convenient distribution of surface charge densities at the spherical interfaces, selfconsistently interacting with each other as well as with the external field created by the incoming electron, can provide a solution of the surface collective modes. Energy loss spectra in the valence range (a few eV) are obtained for trajectories parallel and perpendicular to the axis of the aligned spheres and the nature of the excitations is studied by analysing the charge density distribution induced at the spheres., This work was supported by the Departamento de Educación del Gobierno Vasco/Eusko Jaurlaritza, the University of the Basque Country, and Iberdrola S.A. One of us (J.A.) thanks the Hezkuntza, Ikerketa eta Unibertsitate Saila for financial support.

We investigate the elongation and breaking process of metallic nanowires using the ultimate jellium model in self-consistent density-functional calculations of the electronic structure. In this model the positive background charge deforms to follow the electron density and the energy minimization determines the shape of the system. However, we restrict the shape of the wires by assuming rotational invariance about the wire axis. First, we study the stability of infinite wires and show that the quantum-mechanical shell structure stabilizes the uniform cylindrical geometry at the given magic radii. Next, we focus on finite nanowires supported by leads modeled by freezing the shape of a uniform wire outside the constriction volume. We calculate the conductance during the elongation process using the adiabatic approximation and the WKB transmission formula. We also observe the correlated oscillations of the elongation force. In different stages of the elongation process two kinds of electronic structures appear: one with extended states throughout the wire and one with an atom-cluster-like unit in the constriction and with well-localized states. We discuss the origin of these structures., One of the authors E.O. acknowledges the Spanish Ministerio de Ciencia y Tecnologia for financial support under the Project No. PB98-0870-C02. T.T. acknowledges financial support from the Vilho, Yrjo, and Kalle Vaisala foundation. This work has also been supported by the Academy of Finland through its Center of Excellence Program 2000–2005.