Skip to main content
Log in

The role of power-law correlated disorder in the Anderson metal-insulator transition

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We study the influence of scale-free correlated disorder on the metal-insulator transition in the Anderson model of localization. We use standard transfer matrix calculations and perform finite-size scaling of the largest inverse Lyapunov exponent to obtain the localization length for respective 3D tight-binding systems. The density of states is obtained from the full spectrum of eigenenergies of the Anderson Hamiltonian. We discuss the phase diagram of the metal-insulator transition and the influence of the correlated disorder on the critical exponents.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Broadbent, J. Hammersley, Proc. Camb. Philos. Soc. 53, 629 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    Article  ADS  Google Scholar 

  3. J.W. Essam, Rep. Prog. Phys. 43, 833 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  4. D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992)

  5. M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  6. P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)

    Article  ADS  Google Scholar 

  7. B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)

    Article  ADS  Google Scholar 

  8. C.K. Peng, S. Buldyrev, A. Goldberger, S. Havlin, F. Sciortino, M. Simons, H.E. Stanley, Nature 356, 168 (1992)

    Article  ADS  Google Scholar 

  9. A.M. Vidales, E. Miranda, M. Nazzarro, V. Mayagoitia, F. Rojas, G. Zgrablich, Europhys. Lett. 36, 259 (1996)

    Article  ADS  Google Scholar 

  10. A.B. Harris, J. Phys. C 7, 1671 (1974)

    Article  ADS  Google Scholar 

  11. A.B. Harris, Z. Phys. B 49, 347 (1983)

    Article  ADS  Google Scholar 

  12. A. Weinrib, B.I. Halperin, Phys. Rev. B 27, 413 (1983)

    Article  ADS  Google Scholar 

  13. A. Weinrib, Phys. Rev. B 29, 387 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  14. M.L. Ndawana, R.A. Römer, M. Schreiber, Europhys. Lett. 68, 678 (2004)

    Article  ADS  Google Scholar 

  15. K. Slevin, T. Ohtsuki, Phys. Rev. Lett. 82, 382 (1999)

    Article  ADS  Google Scholar 

  16. T. Ohtsuki, K. Slevin, T. Kawarabayashi, Ann. Phys. (Leipzig) 8, 655 (1999)

    Article  ADS  MATH  Google Scholar 

  17. R.A. Römer, M. Schreiber, The Anderson Transition and its Ramifications – Localisation, Quantum Interference, and Interactions, in Numerical investigations of scaling at the Anderson transition, edited by T. Brandes, S. Kettemann (Springer, Berlin, 2003), pp. 3–19

  18. I. Goldsheid, S. Molcanov, L. Pastur, Funct. Anal. Appl. 11, 1 (1977)

    Article  Google Scholar 

  19. D.J. Thouless, in Ill-condensed Matter, edited by G. Toulouse, R. Balian (North-Holland, Amsterdam, 1979), p. 1

  20. L. Pastur, A. Figotin, Spectra of Random and Almost-Periodic Operators (Springer, Berlin, 1992)

  21. F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999)

    Article  ADS  Google Scholar 

  22. B. Derrida, E. Gardner, J. Phys. 45, 1283 (1984)

    Article  MathSciNet  Google Scholar 

  23. S. Russ, S. Havlin, I. Webman, Philos. Mag. B 77, 1449 (1998)

    ADS  Google Scholar 

  24. A.M. García-García, E. Cuevas, Phys. Rev. B 79, 073104 (2009)

    Article  ADS  Google Scholar 

  25. D.H. Dunlap, H.-L. Wu, P.W. Phillips, Phys. Rev. Lett. 65, 88 (1990)

    Article  ADS  Google Scholar 

  26. H.A. Makse, S. Havlin, M. Schwartz, H.E. Stanley, Phys. Rev. E 53, 5445 (1996)

    Article  ADS  Google Scholar 

  27. F. Milde, R.A. Römer, M. Schreiber, Phys. Rev. B 61, 6028 (2000)

    Article  ADS  Google Scholar 

  28. A. MacKinnon, B. Kramer, Phys. Rev. Lett. 47, 1546 (1981)

    Article  ADS  Google Scholar 

  29. A. MacKinnon, B. Kramer, Z. Phys. B 53, 1 (1983)

    Article  ADS  Google Scholar 

  30. A. Croy, P. Cain, M. Schreiber, Eur. Phys. J. B 82, 107 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  31. B. Bulka, M. Schreiber, B. Kramer, Z. Phys. B 66, 21 (1987)

    Article  ADS  Google Scholar 

  32. B. Kramer, K. Broderix, A. Mackinnon, M. Schreiber, Physica A 167, 163 (1990)

    Article  ADS  Google Scholar 

  33. J. Brndiar, P. Markoš, Phys. Rev. B 74, 153103 (2006)

    Article  ADS  Google Scholar 

  34. J.L. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, 1996)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Croy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Croy, A., Cain, P. & Schreiber, M. The role of power-law correlated disorder in the Anderson metal-insulator transition. Eur. Phys. J. B 85, 165 (2012). https://doi.org/10.1140/epjb/e2012-21059-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-21059-6

Keywords

Navigation