Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Metal–insulator transition in chains with correlated disorder

A Retraction to this article was published on 13 February 2003

Abstract

According to Bloch's theorem, electronic wavefunctions in perfectly ordered crystals are extended, which implies that the probability of finding an electron is the same over the entire crystal1. Such extended states can lead to metallic behaviour. But when disorder is introduced in the crystal, electron states can become localized, and the system can undergo a metal–insulator transition (also known as an Anderson transition)2,3,4. Here we theoretically investigate the effect on the physical properties of the electron wavefunctions of introducing long-range correlations in the disorder in one-dimensional binary solids, and find a correlation-induced metal–insulator transition. We perform numerical simulations using a one-dimensional tight-binding model, and find a threshold value for the exponent characterizing the long-range correlations of the system. Above this threshold, and in the thermodynamic limit, the system behaves as a conductor within a broad energy band; below threshold, the system behaves as an insulator. We discuss the possible relevance of this result for electronic transport in DNA, which displays long-range correlations5,6 and has recently been reported to be a one-dimensional disordered conductor7,8,9,10.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Wavefunctions for periodic, disordered and correlated-disordered chains.
Figure 2: Localization length behaviour in correlated-disordered chains.
Figure 3: Density of states and scaling exponent as a function of the correlations.
Figure 4: Results in DNA.

References

  1. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Holt-Saunders, London, 1976)

    MATH  Google Scholar 

  2. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)

    ADS  CAS  Article  Google Scholar 

  3. Kramer, B. & MacKinnon, A. Localization: theory and experiment. Rep. Prog. Phys. 56, 1469–1564 (1993)

    ADS  CAS  Article  Google Scholar 

  4. Janssen, M. Statistics and scaling in disordered mesoscopic electron-systems. Phys. Rep. 295, 1–91 (1998)

    ADS  CAS  Article  Google Scholar 

  5. Peng, C.-K. et al. Long-range correlations in nucleotide sequences. Nature 356, 168–170 (1992)

    ADS  CAS  Article  Google Scholar 

  6. Holste, D., Grosse, I. & Herzel, H. Statistical analysis of the DNA sequence of human chromosome 22. Phys. Rev. E 64, 041917 (2001)

  7. Fink, H. V. & Schönenberger, C. Electrical conduction through DNA molecules. Nature 398, 407–410 (1999)

    ADS  CAS  Article  Google Scholar 

  8. Henderson, P. T., Jones, D., Hampikian, G., Kan, Y. & Schuster, G. B. Long distance charge transport in duplex DNA: The phonon-assisted polaron-like hopping mechanism. Proc. Natl Acad. Sci. USA 96, 8353–8358 (1999)

    ADS  CAS  Article  Google Scholar 

  9. Porath, D., Bezryadin, A., de Vries, S. & Dekker, C. Direct measurement of electrical transport through DNA molecules. Nature 403, 635–638 (2000)

    ADS  CAS  Article  Google Scholar 

  10. Hjort, M. & Stafstrom, S. Band resonant tunnelling in DNA molecules. Phys. Rev. Lett. 87, 228101 (2001)

    ADS  CAS  Article  Google Scholar 

  11. Mackinnon, A. & Kramer, B. One-parameter scaling of localization length and conductance in disordered systems. Phys. Rev. Lett. 47, 1546–1549 (1981)

    ADS  Article  Google Scholar 

  12. Hofstetter, E. & Schreiber, M. Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson hamiltonian. Phys. Rev. B 48, 16979–16985 (1993)

    ADS  CAS  Article  Google Scholar 

  13. Kravchenko, S. V., Simonian, D., Sarachik, M. P., Mason, W. & Furneaux, J. E. Electric-field scaling at a B = 0 metal-insulator transition in 2 dimensions. Phys. Rev. Lett. 77, 4398–4941 (1996)

    Article  Google Scholar 

  14. Weymer, A. & Janssen, M. Localization length exponent, critical conductance distribution and mulifractality in hierarchical networks models for the quantum Hall-effect. Ann. Phys. (Leipzig) 7, 159–173 (1998)

    ADS  Article  Google Scholar 

  15. Schweitzer, L. & Zharekeshev, I. Kh. Scaling of level statistics and critical exponent of disordered 2-dimensional symplectic systems. J. Phys. Condens. Matter 9, L441–L445 (1997)

    ADS  CAS  Article  Google Scholar 

  16. Mott, N. F. & Twose, W. The theory of impurity conduction. Adv. Phys. 10, 107–163 (1961)

    ADS  CAS  Article  Google Scholar 

  17. Abou-Chacra, R., Anderson, P. W. & Thouless, D. J. A selfconsistent theory of localization. J. Phys. C 6, 1734–1752 (1973)

    ADS  Article  Google Scholar 

  18. Ishii, K. & Matsuda, H. Localization of normal modes and energy transport in the disordered harmonic chain. Prog. Theor. Phys. Suppl. 45, 56–86 (1970)

    ADS  MathSciNet  Article  Google Scholar 

  19. Davids, P. S. Lyapunov exponents and transfer-matrix spectrum of the random binary alloy. Phys. Rev. B 52, 4146–4155 (1995)

    ADS  CAS  Article  Google Scholar 

  20. Dunlap, D. H., Wu, H.-L. & Phillips, P. Absence of localization in a random-dimer model. Phys. Rev. Lett. 65, 88–91 (1990)

    ADS  CAS  Article  Google Scholar 

  21. Phillips, P. & Wu, H.-L. Localization and its absence: a new metallic state for conducting polymers. Science 252, 1805–1812 (1991)

    ADS  CAS  Article  Google Scholar 

  22. de Moura, F. A. B. F. & Lyra, M. L. Delocalization in the 1D Anderson model with long-range correlated disorder. Phys. Rev. Lett. 81, 3735–3738 (1998)

    ADS  CAS  Article  Google Scholar 

  23. Kantelhardt, J. W., Russ, S., Bunde, A., Havlin, S. & Webman, I. Comment on delocalization in the 1 D Anderson model with long-range correlated disorder. Phys. Rev. Lett. 84, 198–201 (2000)

    ADS  CAS  Article  Google Scholar 

  24. Makse, H. A., Havlin, S., Schwartz, M. & Stanley, H. E. Method for generating long-range correlations for large systems. Phys. Rev. E 53, 5445–5449 (1996)

    ADS  CAS  Article  Google Scholar 

  25. Hu, K., Ivanov, P. Ch., Chen, Z., Carpena, P. & Stanley, H. E. Effect of trends on detrended fluctuation analysis. Phys. Rev. E 64, 011114 (2001)

    ADS  CAS  Article  Google Scholar 

  26. Chen, Z., Ivanov, P. Ch., Hu, K. & Stanley, H. E. Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E 65, 041107 (2002)

    ADS  Article  Google Scholar 

  27. Dandliker, P. J., Holmlin, R. E. & Barton, J. K. Oxidative thymine dimer repair in the DNA helix. Science 275, 1465–1468 (1997)

    CAS  Article  Google Scholar 

  28. Kasumov, A. I. et al. Proximity-induced superconductivity in DNA. Science 291, 280–282 (2001)

    ADS  CAS  Article  Google Scholar 

  29. de Pablo, P. J. et al. Absence of dc-conductivity in λ-DNA. Phys. Rev. Lett 85, 4992–4995 (2000)

    ADS  CAS  Article  Google Scholar 

  30. Yoo, K.-H. et al. Electrical conduction through poly(dA)-poly(dT) and poly(dG)-poly(dC) DNA molecules. Phys. Rev. Lett 87, 198102 (2001)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank L. Cruz for discussions, and the Spanish Ministerio de Educación y Cultura and NIH/National Center for Research Resources for support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pedro Carpena.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Carpena, P., Bernaola-Galván, P., Ivanov, P. et al. Metal–insulator transition in chains with correlated disorder. Nature 418, 955–959 (2002). https://doi.org/10.1038/nature00948

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature00948

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing