Skip to main content
SpringerLink
Log in

Electronic properties of one-dimensional quasiperiodic lattices: Green's function renormalization group approach

  • Original Contributions
  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

Using the inflation-deflation symmetry, we have developed a new real-space decimation approach to study the electronic properties of one-dimensional quasiperiodic lattices. The key result is the construction of a compact renormalization group that allows simple calculation of the average Green's function and the average density of states to any degree. The Fibonacci and the generalized Fibonacci lattices are used to demonstrate the method. Numerical results for the average density of states of these lattices show a good agreement with the results obtained by other methods. This confirms the validity and the efficiency of the approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kohmoto, M., Kadanoff, L.P., Tang, C.: Phys. Rev. Lett.50, 1870 (1983)

    Google Scholar 

  2. Ostlund, S., Pandit, R., Rand, D., Schellnhuber, H.J., Siggia, E.D.: Phys. Rev. Lett.:50, 1873 (1983)

    Google Scholar 

  3. Luck, J.M., Petritis, D.: J. Stat. Phys.42, 289 (1986)

    Google Scholar 

  4. Würtz, D., schneider, T., Politi, A.: Phys. Lett. A129, 88 (1988)

    Google Scholar 

  5. Lu, J.P., Odagaki, T., Birman, J.L.: Phys. Rev. B33, 4809 (1986)

    Google Scholar 

  6. Sire, C., Mosseri, R.: J. Phys. (Paris)51, 1569 (1990)

    Google Scholar 

  7. Niu, Q., Nori, F.: Phys. Rev. Lett.57, 2057 (1986)

    Google Scholar 

  8. Liu, Y., Sritrakool, W.: Phys. Rev. B43, 1110 (1991)

    Google Scholar 

  9. Gumbs, G., Ali, M.K.: Phys. Rev. Lett.60, 1081 (1988)

    Google Scholar 

  10. Holzer, M.: Phys. Rev. B38, 1079 (1988)

    Google Scholar 

  11. Kolár, M., Ali, M.K.: Phys. Rev. B41, 7108 (1990)

    Google Scholar 

  12. You, J.Q., Yang, Q.B.: J. Phys.2, 2093 (1990)

    Google Scholar 

  13. You, J.Q., Yan, J.R., Xie, T., Zeng, X., Zhong, J.X.: J. Phys.3, 7255 (1991)

    Google Scholar 

  14. Severin, M., Riklund, R.: J. Phys.1, 5607 (1989)

    Google Scholar 

  15. Mookerjee, A., Singh, V.A.: Phys. Rev. B34, 7433 (1986)

    Google Scholar 

  16. Haydock, R., Heine, V., Kelly, M.J.: J. Phys. C5, 2845 (1972)

    Google Scholar 

  17. Ashraff, J.A., Stinchcombe, R.B.: Phys. Rev. B37, 5723 (1988)

    Google Scholar 

  18. Chakrabarti, A., Karmakar, S.N., Moitra, R.K.: Phys. Rev. B39, 9370 (1989)

    Google Scholar 

  19. Zhong, J.X., You, J.Q., Yan, J.R., Yan, X.H.: Phys. Rev. B43, 13778 (1991)

    Google Scholar 

  20. Zhong, J.X., Yan, J.R., Yan, X.H., You, J.Q.: J. Phys.3, 5685 (1991)

    Google Scholar 

  21. Zhong, J.X., Yan, J.R., You, J.Q.: J. Phys. A24, L949 (1991)

    Google Scholar 

  22. Chakrabarti, A., Karmakar, S.N.: Phys. Rev. B44, 896 (1991)

    Google Scholar 

  23. Andrade, R.F.S., Schellnhuber, H.J.: Phys. Rev. B44, 13213 (1991)

    Google Scholar 

  24. Zhong, J.X., Xie, T., You, J.Q., Yan, J.R.: Z. Phys.87, 223 (1992)

    Google Scholar 

  25. Newman, M.E.J.: Phys. Rev. B43, 10915 (1991)

    Google Scholar 

  26. Zhong, J.X., You, J.Q., Yan, J.R.: J. Phys.4, 5959 (1992)

    Google Scholar 

  27. You, J.Q., Yan, J.R., Zhong, J.X., Yan, X.H.: Europhys. Lett.17, 231 (1992)

    Google Scholar 

  28. Goncalves da Silva, C.E.T., Koiller, B.: Solid State Commun.40, 215 (1981)

    Google Scholar 

  29. Southern, B.W., Kumar, A.A., Loly, P.D., Tremblay, A.M.S.: Phys. Rev. B27, 1405 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. China Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, 100080, Beijing, People's Republic of China

    J. X. Zhong, J. R. Yan & J. Q. You

  2. Laboratory of Modern Physics, Institute of Science and Technology, Xiangtan University, 110015, Xiangtan, Hunan, People's Republic of China

    J. X. Zhong, J. R. Yan, J. Q. You, X. H. Yan & Y. P. Mei

  3. Laboratory of Atomic Imaging of Solids, Institute of Metal Research, Chinese Academy of Sciences, 110015, Shengyang, People's Republic of China

    J. X. Zhong & J. Q. You

Authors
  1. J. X. Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Q. You
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. X. H. Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. P. Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhong, J.X., Yan, J.R., You, J.Q. et al. Electronic properties of one-dimensional quasiperiodic lattices: Green's function renormalization group approach. Z. Physik B - Condensed Matter 91, 127–133 (1993). https://doi.org/10.1007/BF01316714

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01316714

Keywords

Search

Navigation