Periodic orbit theory for realistic cluster potentials: The leptodermous expansion

The formation of supershells observed in large metal clusters can be qualitatively understood from a periodic-orbit-expansion for a spherical cavity. To describe the changes in the supershell structure for different materials, one has, however, to go beyond that simple model. We show how periodic-orbit-expansions for realistic cluster potentials can be derived by expanding only the classical radial action around the limiting case of a spherical potential well. We give analytical results for the leptodermous expansion of Woods-Saxon potentials and show that it describes the shift of the supershells as the surface of a cluster potential gets softer. As a byproduct of our work, we find that the electronic shell and supershell structure is not affected by a lattice contraction, which might be present in small clusters.Comment: 15 pages RevTex, 11 eps figures, additional information at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/users/koch/Diss

Supershells in Metal Clusters: Self-Consistent Calculations and their Semiclassical Interpretation

To understand the electronic shell- and supershell-structure in large metal clusters we have performed self-consistent calculations in the homogeneous, spherical jellium model for a variety of different materials. A scaling analysis of the results reveals a surprisingly simple dependence of the supershells on the jellium density. It is shown how this can be understood in the framework of a periodic-orbit-expansion by analytically extending the well-known semiclassical treatment of a spherical cavity to more realistic potentials.Comment: 4 pages, revtex, 3 eps figures included, for additional information see http://radix2.mpi-stuttgart.mpg.de/koch/Diss

Mechanisms of resonant low frequency Raman scattering from metallic nanoparticle Lamb modes

International audienceThe low frequency Raman scattering from gold nanoparticle bimodal assemblies with controlled size distributions has been studied. Special care has been paid to determining the size dependence of the Raman intensity corresponding to the quadrupolar Lamb mode. Existing models based on a microscopic description of the scattering mechanism in small particles (bond polarizability, dipole induced dipole models) predict, for any Raman-active Lamb modes, an inelastic intensity scaling as the volume of the nanoparticle. Surprisingly experimental intensity ratios are found to be anomalously much greater than theoretical ones, calling into question this scaling law. To explain these discrepancies, a simple mechanism of Raman scattering, based on the density fluctuations in the nanoparticles induced by the Lamb modes, is introduced. This modeling, in which the nanoparticle is described as an elastic isotropic continuous medium-as in Lamb theory, successfully explains the major features exhibited by low frequency Raman modes. Moreover this model provides a unified picture for any material, suitable for handling both small and large size ranges, as well as non-resonant and resonant excitation conditions in the case of metallic species. Published by AIP Publishing

Oscillatory Size-Dependence of the Surface Plasmon Linewidth in Metallic Nanoparticles

We study the linewidth of the surface plasmon resonance in the optical absorption spectrum of metallic nanoparticles, when the decay into electron-hole pairs is the dominant channel. Within a semiclassical approach, we find that the electron-hole density-density correlation oscillates as a function of the size of the particles, leading to oscillations of the linewidth. This result is confirmed numerically for alkali and noble metal particles. While the linewidth can increase strongly, the oscillations persist when the particles are embedded in a matrix.Comment: RevTeX4, 5 pages, 2 figures, final versio

Origin of Shifts in the Surface Plasmon Resonance Frequencies for Au and Ag Nanoparticles

Origin of shifts in the surface plasmon resonance (SPR) frequency for noble metal (Au, Ag) nanoclusters are discussed in this book chapter. Spill out of electron from the Fermi surface is considered as the origin of red shift. On the other hand, both screening of electrons of the noble metal in porous media and quantum effect of screen surface electron are considered for the observed blue shift in the SPR peak position.Comment: 37 pages, 14 Figures in the submitted book chapter of The Annual Reviews in Plasmonics, edited by Professor Chris D. Geddes. Springer Scinec

Resonant Raman Scattering by quadrupolar vibrations of Ni-Ag Core-shell Nanoparticles

Low-frequency Raman scattering experiments have been performed on thin films consisting of nickel-silver composite nanoparticles embedded in alumina matrix. It is observed that the Raman scattering by the quadrupolar modes, strongly enhanced when the light excitation is resonant with the surface dipolar excitation, is mainly governed by the silver electron contribution to the plasmon excitation. The Raman results are in agreement with a core-shell structure of the nanoparticles, the silver shell being loosely bonded to the nickel core.Comment: 3 figures. To be published in Phys. Rev.

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

Twist Mode in Spherical Alkali Metal Clusters

A remarkable orbital quadrupole magnetic resonance, so-called twist mode, is predicted in alkali metal clusters where it is represented by $I^{\pi}=2^-$ low-energy excitations of valence electrons with strong M2 transitions to the ground state. We treat the twist by both macroscopic and microscopic ways. In the latter case, the shell structure of clusters is fully exploited, which is crucial for the considered size region ($8\le N_e\le 1314$). The energy-weighted sum rule is derived for the pseudo-Hamiltonian. In medium and heavy spherical clusters the twist dominates over its spin-dipole counterpart and becomes the most strong multipole magnetic mode.Comment: 8 pages, 4 figures, to be published in Phys. Rev. Lett., v.85, n.15, 200

On the 3n+l Quantum Number in the Cluster Problem

It has recently been suggested that an exactly solvable problem characterized by a new quantum number may underlie the electronic shell structure observed in the mass spectra of medium-sized sodium clusters. We investigate whether the conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l and 2n+l, which characterize the hydrogen problem and the isotropic harmonic oscillator in three dimensions.Comment: 8 pages, revtex, 4 eps figures included, to be published in Phys.Rev.A, additional material available at http://radix2.mpi-stuttgart.mpg.de/koch/Diss

Atomic-scale confinement of optical fields

In the presence of matter there is no fundamental limit preventing confinement of visible light even down to atomic scales. Achieving such confinement and the corresponding intensity enhancement inevitably requires simultaneous control over atomic-scale details of material structures and over the optical modes that such structures support. By means of self-assembly we have obtained side-by-side aligned gold nanorod dimers with robust atomically-defined gaps reaching below 0.5 nm. The existence of atomically-confined light fields in these gaps is demonstrated by observing extreme Coulomb splitting of corresponding symmetric and anti-symmetric dimer eigenmodes of more than 800 meV in white-light scattering experiments. Our results open new perspectives for atomically-resolved spectroscopic imaging, deeply nonlinear optics, ultra-sensing, cavity optomechanics as well as for the realization of novel quantum-optical devices