Abstract
The response of a spherical metallic particle and a void in a metal on an arbitrary external electrical (gradient) field is given analytically within two models: a macroscopic dielectric description in terms of dielectric functions and a linearized hydrodynamic theory which takes into account boundary effects as well as spatial dispersion. From the response functions, the eigenfrequencies of the collective modes and the electron-energy-loss function are obtained. For small radii we found collective modes extending beyond the classical ℓ = ∞ limit of surface-plasmons up to the volume-plasmon. Concerning electron-energy-losses, our results demonstrate that the “blue-shift” on the collective modes which were observed in potassium clusters or calculated for voids in metals are almost of classical origin and stem from spatial dispersion.
Similar content being viewed by others
References
Perenboom, J.A.A.J., Wyder, P., and Meier, F., Phys. Rep.78, 174 (1981)
Kreibig, U. and Genzel, L., Surf. Sci.156, 678 (1985)
Halperin, W., Rev. Mod. Phys.58, 533 (1986).
Brack, M., Rev. Mod. Phys.65, 677 (1993).
Mie, G., Ann. Phys. (Leipzig)25, 377 (1908). see: Born, M. and Wolf, E.,Principles of Optics, Pergamon (1959) p. 630.
Crowell, J. and Ritchie, R.H., Phys. Rev.172, 436 (1968).
Ferrell, T.L. and Echinique, P.M., Phys. Rev. Lett.55, 1526 (1985); Ferrell, T.L., Warmack, R.J., Anderson, V.E. and Echinique, P.M., Phys. Rev.B35, 7365 (1987).
Kramer, B., Ed.Quantum Coherence in Mesoscopic Systems, Nato ASI, series B, Phys. Vol. 254, Plenum, (1991).
Ekardt, W., Phys. Rev.B32, 1961 (1985),B33, 8803 (1986),B36, 4483 (1987)
Beck, D.E., Phys. Rev.B43, 7301 (1991).
Bloch, F., Z. Phys.81, 363 (1933).
Forstmann, F. and Stenschke, H., Phys. Rev. Lett.38, 1365 (1977), Phys. RevB17, 1489, (1978), and references cited therein.
Jensen, H., Z. Phys.106, 620 (1937).
Fujimoto, F. and Komaki, K., J. Phys. Soc. Jap.25, 1679 (1968).
Lushnikov, A.A. and Simonov, A.J., Z. Phys.270, 17 (1974),B21, 357 (1975).
Ashley, J.C. and Ferrell, T.L., Phys. Rev.B14, 3277 (1976).
Boardman, A.D. and Paranjape, B.V., J. Phys.F 7, 1935 (1977).
Aers, G.C., Paranjape, B.V., and Boardman, A.D., Jour. Phys. Chem. Solids40, 319, (1979).
Barberán, N. and Bausells, J., Phys. Rev.B31, 6354 (1985).
Tran Thoai, D.B., phys. stat. sol. (b)136, 291 (1986).
Penn, D.R. and Apell, P., J. Phys. C16, 5729 (1983).
Feibelman, P.J., Prog. Surf. Sci.12, 287 (1982).
Penn, D.R. and Rendell, P.W., Phys. Rev. Lett.47, 1067 (1981).
Tanner, D.B., Phys. Rev.30, 1042 (1984).
Hua, Xia Ming and Gersten, J.F., Phys. Rev.B31, 855, (1985).
vom Felde, A., Fink, J., and Ekardt, W., Phys. Rev. Lett.61, 2249 (1988).
Keldysh, L.V., Kirshnits, D.A., and Maradudin, A.A., Eds.The dielectric function of condensed systems. North Holland (1989).
Jackson, J.D.,Classical Electrodynamics, Wiley (1962).
Abramowitz, M. and Stegun, I.Handbook of Mathematical Functions, Dover Publications, INC, New York (1968).
Zohm, H.,Linearer Response eines Metallkügelchens und Verlustfunktion für Elektronenemergieverlustspektroskopie, Diplomarbeit, Universität Karlsruhe (1988), unpublished.
Mensch, M.,Größenabhängigkeit der dielektrischen Eigenschaften kugel-förmiger Metallcluster, Diplomarbeit, Universität Karlsruhe (1990), unpublished.
Hall, R.B., Am. J. Phys.31, 696 (1963).
Melnyk, A.R. and Harrison, M.J., Phys. Rev. Lett.21, 85 (1968).
vom Felde, A., Sprösser-Prou, J., and Fink, J., Phys. Rev.B40, 10181 (1989).
Genzel, L., Martin, T., and Kreibig, U., Z. Phys.B21, 339 (1975).
Wu, King-Sum David and Beck, D.E., Phys. Rev.B36, 998 (1987).
Serra, LI, Garcias, F., Navarro, J., Barberán, N., Barranco, M., and Pi, M., Phys. Rev.B46, 9369 (1992).
Fink, J.,Advances in Electronics and Electron Physics, Vol. 75, p. 121, Academic Press. (1989).
Egerton, R.F.,Electron Energy Loss Spectroscopy in the Electron Microscope. Plenum Press, New York (1986).
Kreibig, u. and Zacharias, P. Z. Physik231, 128 (1970).
Das, P.C. and Gersten, J.I., Phys. Rev.B27, 5412 (1983).
Natta, M., Sol. State Commun.7, 823 (1969).
Manzke, R, Crezelius, G, and Fink, J, Phys. Rev. Lett51 1095 (1983).
vom Felde, A, Fink, J, Müller-Heinzerling, Th, Pflüger, J, Scheer, B, Linker, G, and Kaletta, D, Phys. Rev. Lett53, 922 (1984).
Sprösser-Prou, J., vom Felde, A., and Fink, J., Phys. Rev.40, 5799 (1989).
Daniels, A., v. Festenberg, C., Raether, H., and Zeppenfeld, K.,Springer Tracts in Modern Physics 54, 57, (1970).
Apell, P. and Ljungbert, Å., Sol. State Commun.46, 47 (1983).
Saito, S., Bertsch, G.F. and Tománek, D., Phys. Rev.B43, 6804 (1991).
Brechignac, C., Cahuzac, Ph., Kebaili, N., Leygnier, J., and Sarfati, A., Phys. Rev. Lett.68, 3916 (1992).
Malov, Yu, A, and Zaretzky, D.F., Phys. LettA177, 379 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
v. Baltz, R., Mensch, M. & Zohm, H. Longitudinal electric response and loss-function of metallic microspheres and voids. Z. Physik B - Condensed Matter 98, 151–161 (1995). https://doi.org/10.1007/BF01324520
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01324520