Abstract
Friedel oscillations1 are spatial modulations of the electron density n(r) which occur in microscopic zero-temperature calculations of metallic properties, whenever the metal is subject to a local disturbance. Static Friedel oscillations take the form of a standing-wavelike perturbation in the electron density, falling off with distance from the disturbance. These oscillations are most clearly derived in the jellium model in which the positive metal ions are represented by a uniform positive background. This suppresses periodic crystalline density oscillations and leaves the Friedel oscillations plainly visible. One example is provided by the electron density profile n(z) in calculations2 of the jellium metal surface (Fig. 1): here the surface itself constitutes the “disturbance”, and the wavenumber of the oscillations is twice the Fermi momentum in the bulk metal, 2kF. The oscillations die as z−2 where −z is the depth into the metal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Friedel, Phil. Mag. 43, 153 (1952).
N.D. Lang and W. Kohn, Phys. Rev. B 1, 4555 (1970).
N.D. Lang, Adv. Sol. State Phys. 28, 225 (1973).
W.A. Harrison, “Solid State Theory”, McGraw Hill, New York 1970, p. 299.
E. Bruno & B. L. Gyorffy PRL 71, 181 (1993).
L.M. Roth, H.J. Zeigler and T.A. Kaplan, Phys. Rev. 149, 519 (1966)
W. Kohn, Phys. Rev. Lett. 2, 393 (1959).
J.M. Ziman, “Principles of the Theory of Solids”, Cambridge University Press, Cambridge, 1972.
W.R. Bennet, W. Schwarzacher and W.F. Egelhoff, Phys. Rev. Lett. 65, 3169 (1990).
J. Unguris, RJ. Celotta and D. T. Pierce, Phys. Rev. Lett. 67, 140 (1991).
P. Bruno and C. Chappert, Phys. Rev. Lett. 67, 1602 (1991): Phys. Rev. B 46, 261 (1992).
V. Grolier, D. Renard, B. Bartenlian, P. Beauvillain, C. Chappert, C. Dupas, J. Ferr é, M. Galtier, E. Kolb, M. Mulloy, J.P. Renard and P. Veillet, Phys. Rev. Lett 71, 3023 (1993).
N.E. Bickers, DJ. Scalapino and R.T. Scalettar, Internat. J. Mod. Phys. B 1, 687 (1987).
N.E. Bickers, DJ. Scalapino and S.R. White, Phys. Rev. Lett. 62, 961 (1989).
F.K. Schulte, Surf. Sci. 55, 427 (1976).
J.F. Dobson, Phys. Rev. B 46, 10163 (1992).
W. Kohn and L.J. Sham, Phys. Rev. 137, A1697 (1965).
K.-D. Tsuei, E.W. Plummer and PJ. Feibelman, Phys. Rev. Lett. 63, 2256 (1989).
K.-D. Tsuei, E.W. Plummer, A. Liebsch, K. Kempa and P. Bakshi, Phys. Rev. Lett. 64, 44 (1990).
P.R. Pinsukanjana, E.G. Gwinn, J.F. Dobson, E.L. Yuh, N.G. Asmar, M. Sundaram, and A.C. Gossard, Phys. Rev. B 46, 7284 (1992).
W. Kohn and LJ. Sham, Phys. Rev. 140, A1133 (1965).
A.L. Fetter and J.D. Walecka, “Quantum Theory of Many-Particle Systems”, McGraw-Hill, New York 1971.
T. Ando, Z. Phys. B 26, 263 (1977).
A. Zangwill and P. Soven, Phys. Rev. A 21, 1561 (1980).
E. Runge and E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984).
E.K.U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985): erratum ibid., 57, 923 (1986).
N. Iwamoto and E.K.U. Gross, Phys. Rev. B 35, 3003 (1987).
J.F. Dobson and G. H. Harris, J. Phys. C: Solid St. Phys. 21, L729 (1988).
B.NJ. Persson, J. Phys. C: Solid St. Phys. 13, 435 (1980).
PJ. Feibelman, Prog. Surf. Sci. 12, 287 (1982).
PJ. Feibelman, Phys. Rev. B 9, 5077 (1974): Phys. Rev. B 12, 1319 (1975).
J.F. Dobson and G.H. Harris, J. Phys. C: Solid St. Phys 19, 3971 (1986).
K. Kempa and W.L. Schaich, Phys. Rev. B 34, 547 (1986).
K. Kempa and W.L. Schaich, Phys. Rev. B 37, 6711 (1988).
K. Kempa, A. Liebsch and W.L. Schaich, Phys. Rev. B 38, 12645 (1988).
A. Liebsch, Phys. Rev. B 36, 7378 (1987).
K.J. Song, D. Heskett, H.L. Dai, A. Liebsch, and E.W. Plummer, Phys. Rev. Lett. 61, 1380 (1988).
K. Burke and W.L. Schaich, Phys. Rev. B 48, 14599 (1993).
W.L. Schaich, private communication (1993).
A. Liebsch, Phys. Rev. Lett. 67, 2858 (1991).
G.H. Harris “Electronic properties of juxtaposed metal surfaces”, Ph.D. thesis, Griffith University, Nathan, Queensland Australia 1992.
A.G. Eguiluz, Phys. Rev. Lett. 51, 1907 (1983).
R.S. Sorbello, Solid State Commun. 56, 821 (1985): ibid 48, 989 (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Dobson, J.F. (1995). Friedel Oscillations in Condensed Matter Calculations. In: Neilson, D., Das, M.P. (eds) Computational Approaches to Novel Condensed Matter Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9791-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9791-6_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9793-0
Online ISBN: 978-1-4757-9791-6
eBook Packages: Springer Book Archive