Skip to main content
SpringerLink
Log in

Phonons and Electrons in Quasicrystals

  • Chapter
Quasicrystals

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 55))

  • 721 Accesses

Summary

We present methods for ab initio calculations of phonon and electron spectra of quasicrystals and their approximants. The phonon and electron spectra of smaller approximants are calculated by the exact diagonalization of the dynamical matrix and the tight-binding-linear-muffin-tin-orbital (TB-LMTO) Hamiltonian, respectively. The eigenvalue spectra of bigger approximants are calculated by the recursion method. We discuss the results obtained for realistic models of icosahedral and decagonal quasicrystals. We show that the nature of the phonon and electron eigenvalue spectra is closely related to the diffraction pattern of quasicrystals. We investigate the character of propagated and localized phonon states in icosahedral and decagonal approximants. We discuss the formation of the pseudo-gap in the electronic spectrum and its contribution to the structural stability of quasicrystals. We show that highly anomalous transport properties of quasicrystals are related to the almost dispersionless character of the electron-eigenvalue spectrum.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen O.K. (1975): Phys. Rev. B 12, 3060

    Article  ADS  Google Scholar 

  2. Andersen O.K., Jepsen D., Sob M. (1987): In Electronic Band Structure and its Applications, ed. M. Youssouff, Springer, Berlin

    Google Scholar 

  3. Arai M., Tokihiro T., Fujiwara T., Kohomoto M. (1988): Phys. Rev. B 38, 1621

    Article  MathSciNet  ADS  Google Scholar 

  4. Basov D.N., Pierce F.S., Volkov P., Poon S.J., Timusk T. (1994): Phys. Rev. Lett. 73, 1865

    Article  ADS  Google Scholar 

  5. Bienenstock A., Ewald P.P. (1962): Acta Crystall. 15, 1253

    Article  MathSciNet  Google Scholar 

  6. Boissieu M. de, Boudard M., Moudden M., Quilichini M., Bellisent R., Hennion B., Currat R., Janot Ch. (1993): J. Non-Cryst. Solids, 153 & 154, 552

    Article  Google Scholar 

  7. Burkov S.E. (1991): Phys. Rev. Lett. 67, 614

    Article  ADS  Google Scholar 

  8. Burkov S.E. (1991): Phys. Rev. 47, 12 325

    Google Scholar 

  9. Carlsson J.C. (1993): Phys. Rev. B 47, 2515

    Article  ADS  Google Scholar 

  10. Conrad M. (1997) : Tantalreiche Telluride, Thesis, Universität Dortmund (unpublished)

    Google Scholar 

  11. Conrad M., Krumreich F., Harbrecht B. (1998): Angew. Chemie Int. Ed. 37, 1383

    Article  Google Scholar 

  12. Cornier-Quinandon M., Qivy A., Lefebvre S., Elkaim E., Heger G., Katz A., Gratias D. (1991) : Phys. Rev. B 44, 2071

    Article  ADS  Google Scholar 

  13. Dall’Acqua G., Krajčí M., Hafner J. (1997): J. Phys. Cond. Matt. 9, 10725

    Article  ADS  Google Scholar 

  14. Fujiwara T., Arai M., Tokihiro T., Kohomoto M. (1988): Phys. Rev. B 37, 2797

    Article  MathSciNet  ADS  Google Scholar 

  15. Gardner M. (1977) : Sci. Am. 236(1), 110

    Article  ADS  Google Scholar 

  16. Goldmann A.I., Stassis C., Boissieu M. de, Currat R., Janot Ch., Bellisent R., Moudden M., Gayle F.W. (1992): Phys. Rev. B 45, 10280

    Article  ADS  Google Scholar 

  17. Hafner J. (1983): J. Phys. C 16, 5773

    Article  ADS  Google Scholar 

  18. Hafner J. (1987) : From Hamiltonians to Phase Diagrams, Springer, Berlin

    Book  Google Scholar 

  19. Hafner J., Krajčí M. (1993): Phys. Rev. B 47, 1084

    Article  ADS  Google Scholar 

  20. Hafner J., Krajčí M. (1993): Phys. Rev. B 47, 11795

    Article  ADS  Google Scholar 

  21. Hafner J., Krajčí M. (1998): Phys. Rev. B 57, 2849

    Article  ADS  Google Scholar 

  22. Hafner J., Krajčí M. (1999): In Physical Properties of Quasicrystals, ed. Z. M. Stadnik, Springer Series in Solid State Physics Vol. 126, Springer, Berlin, p. 209

    Chapter  Google Scholar 

  23. Hafner J., Krajčí M., Mihalkovič M. (1996): Phys. Rev. Lett. 76, 2738

    Article  ADS  Google Scholar 

  24. Harrison W.A. (1989): Electronic Structure and the Properties of Solids, Dover, New York, p. 359

    Google Scholar 

  25. Haydock R. (1980) : In Solid State Physics, ed. H. Ehrenreich, F. Seitz, D. Turnbull, Academic Press, New York, Vol. 35, 215

    Google Scholar 

  26. Henley C.L., Elser V. (1986): Phil. Mag. B 53, L59

    Article  Google Scholar 

  27. Hiraga K., Sun W. (1993): Phil. Mag. Lett. 7, 11

    Google Scholar 

  28. IUC, International Union of Crystallography (1992) : Acta Crystall. A 48, 928

    Google Scholar 

  29. Krajčí M. (1997): Mat. Sci. Eng. A 226–228, 950

    Article  Google Scholar 

  30. Krajčí M., Fujiwara T. (1988): Phys. Rev. B 38, 12903

    Article  ADS  Google Scholar 

  31. Krajčí M., Hafner J. (1992): Phys. Rev. B 46, 10 669

    Google Scholar 

  32. Krajčí M., Hafner J. (1998): Phys. Rev. B 58, 5378

    Article  ADS  Google Scholar 

  33. Krajčí M., Hafner J. (1998): Phys. Rev. B 58, 14110

    Article  ADS  Google Scholar 

  34. Krajčí M., Hafner J. (1998): In Aperiodic 97, ed. M. de Boissieu, J.-L. VergerGaugry, R. Currat, World Scientific, Singapore, p. 619

    Google Scholar 

  35. Krajčí M., Hafner J. (1999): Phys. Rev. B 59, 8347

    Article  ADS  Google Scholar 

  36. Krajčí M., Hafner J. (2000): J. Phys. Cond. Matt. 12, 5831

    Article  ADS  Google Scholar 

  37. Krajčí M., Hafner J. (2001): J. Phys. Cond. Matt. 13, 3817

    Article  ADS  Google Scholar 

  38. Krajčí M., Hafner J. (2001): to be published

    Google Scholar 

  39. Krajčí M., Hafner J., Mihalkovič M. (1996): Europhys. Lett. 34, 207

    Article  ADS  Google Scholar 

  40. Krajčí M., Hafner J., Mihalkovič M. (1997): Phys. Rev. B 55, 843

    Article  ADS  Google Scholar 

  41. Krajčí M., Hafner J., Mihalkovič M. (1997): Phys. Rev. B 56, 3072

    Article  ADS  Google Scholar 

  42. Krajčí M., Hafner J., Mihalkovič M. (2000): Phys. Rev. B 62, 243

    Article  ADS  Google Scholar 

  43. Krajčí M., Hafner J., Mihalkovič M. (2000): Mat. Sci. Eng. A 294–296, 548

    Article  Google Scholar 

  44. Krajčí M., Windisch M., Hafner J., Kresse G., Mihalkovič M. (1995): Phys. Rev. B 51, 17355

    Article  ADS  Google Scholar 

  45. Lucchini M.U., Nex C.M.M. (1987): J. Phys. C 20, 3125

    Article  ADS  Google Scholar 

  46. Lundqvist S., March N.H. (1983): Theory of the Inhomogeneous Electron Gas, Plenum Press, New York

    Google Scholar 

  47. Martin S., Hebard A.E., Kortan A.R., Thiel F.A. (1991): Phys. Rev. Lett. 67, 719

    Article  ADS  Google Scholar 

  48. Mermin N.D. (1992): Rev. Mod. Phys. 63, 3

    Article  MathSciNet  ADS  Google Scholar 

  49. Nex C.M.M. (1978): J. Phys. A 11, 653

    Article  ADS  MATH  Google Scholar 

  50. Niizeki K. (1990): J. Phys. A 22, 4295

    Article  MathSciNet  ADS  Google Scholar 

  51. Novak H.J., Andersen, O.K., Fujiwara T., Jepsen O., Vargas P. (1991): Phys. Rev. B 44, 3577

    Article  ADS  Google Scholar 

  52. Pierce F.S., Poon S.J., Guo Q. (1994): Phys. Rev. Lett. 73, 2220

    Article  ADS  Google Scholar 

  53. Reich C., Conrad M., Krumreich F., Harbrecht B. (1999): Mat. Res. Soc. Symp. Proc. 553, 83

    Article  Google Scholar 

  54. Rieth T., Schreiber M. (1997) : Z. Phys. B 104, 99

    Article  ADS  Google Scholar 

  55. Rokhhsar D.S., Wright D.C., Mermin N.D. (1988): Phys. Rev. B 37, 8145

    Article  MathSciNet  ADS  Google Scholar 

  56. Skriver H.L. (1984): The LMTO Method, Springer, Berlin

    Book  Google Scholar 

  57. Smith A.P., Ashcroft N.W. (1987): Phys. Rev. Lett. 59, 1356

    ADS  Google Scholar 

  58. Stadnik Z.M., Zhang G.W., Tsai A.P., Inoue A. (1995): Phys. Rev. B 51, 11358

    Article  ADS  Google Scholar 

  59. Trambly de Laissardière G., Fujiwara T. (1994): Phys. Rev. B 50, 9843

    Article  ADS  Google Scholar 

  60. Trambly de Laissardière G., Nguyen Manh D., Magaud L., Julien J.P., CyrotLackmann F, Mayou D. (1995): Phys. Rev. B 52, 7920

    Article  ADS  Google Scholar 

  61. Tsunetsugu H., Fujiwara T., Ueda K., Tokihiro T. (1986): J. Phys. Soc. Jpn. 55, 1420;

    Article  ADS  Google Scholar 

  62. see also Sire C. (1994): In Lectures on Quasicrystals, ed. F. Hippert, D. Gratias, Les Editions de Physique, Les Ulis

    Google Scholar 

  63. Windisch M., Hafner J., Krajčí M., Mihalkovič M. (1994): Phys. Rev. B 49, 8701

    Article  ADS  Google Scholar 

  64. Windisch M., Krajčí M., Hafner J. (1994): J. Phys. Cond. Mat. 6, 6977

    Article  ADS  Google Scholar 

Download references

Authors
  1. Marián Krajčí
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jürgen Hafner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Physik, TU Chemnitz, 09107, Chemnitz, Germany

    Jens-Boie Suck  & Peter Häussler  & 

  2. International University Bremen, Postfach 75 05 61, 28725, Bremen, Germany

    Michael Schreiber

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Krajčí, M., Hafner, J. (2002). Phonons and Electrons in Quasicrystals. In: Suck, JB., Schreiber, M., Häussler, P. (eds) Quasicrystals. Springer Series in Materials Science, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05028-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-05028-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08390-7

  • Online ISBN: 978-3-662-05028-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation