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
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Holt-Saunders, London, 1976)
Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)
Kramer, B. & MacKinnon, A. Localization: theory and experiment. Rep. Prog. Phys. 56, 1469–1564 (1993)
Janssen, M. Statistics and scaling in disordered mesoscopic electron-systems. Phys. Rep. 295, 1–91 (1998)
Peng, C.-K. et al. Long-range correlations in nucleotide sequences. Nature 356, 168–170 (1992)
Holste, D., Grosse, I. & Herzel, H. Statistical analysis of the DNA sequence of human chromosome 22. Phys. Rev. E 64, 041917 (2001)
Fink, H. V. & Schönenberger, C. Electrical conduction through DNA molecules. Nature 398, 407–410 (1999)
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)
Porath, D., Bezryadin, A., de Vries, S. & Dekker, C. Direct measurement of electrical transport through DNA molecules. Nature 403, 635–638 (2000)
Hjort, M. & Stafstrom, S. Band resonant tunnelling in DNA molecules. Phys. Rev. Lett. 87, 228101 (2001)
Mackinnon, A. & Kramer, B. One-parameter scaling of localization length and conductance in disordered systems. Phys. Rev. Lett. 47, 1546–1549 (1981)
Hofstetter, E. & Schreiber, M. Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson hamiltonian. Phys. Rev. B 48, 16979–16985 (1993)
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)
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)
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)
Mott, N. F. & Twose, W. The theory of impurity conduction. Adv. Phys. 10, 107–163 (1961)
Abou-Chacra, R., Anderson, P. W. & Thouless, D. J. A selfconsistent theory of localization. J. Phys. C 6, 1734–1752 (1973)
Ishii, K. & Matsuda, H. Localization of normal modes and energy transport in the disordered harmonic chain. Prog. Theor. Phys. Suppl. 45, 56–86 (1970)
Davids, P. S. Lyapunov exponents and transfer-matrix spectrum of the random binary alloy. Phys. Rev. B 52, 4146–4155 (1995)
Dunlap, D. H., Wu, H.-L. & Phillips, P. Absence of localization in a random-dimer model. Phys. Rev. Lett. 65, 88–91 (1990)
Phillips, P. & Wu, H.-L. Localization and its absence: a new metallic state for conducting polymers. Science 252, 1805–1812 (1991)
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)
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)
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)
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)
Chen, Z., Ivanov, P. Ch., Hu, K. & Stanley, H. E. Effect of nonstationarities on detrended fluctuation analysis. Phys. Rev. E 65, 041107 (2002)
Dandliker, P. J., Holmlin, R. E. & Barton, J. K. Oxidative thymine dimer repair in the DNA helix. Science 275, 1465–1468 (1997)
Kasumov, A. I. et al. Proximity-induced superconductivity in DNA. Science 291, 280–282 (2001)
de Pablo, P. J. et al. Absence of dc-conductivity in λ-DNA. Phys. Rev. Lett 85, 4992–4995 (2000)
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)
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
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no competing financial interests.
Supplementary information
Rights 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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/nature00948
This article is cited by
-
Phenomenon of multiple reentrant localization in a double-stranded helix with transverse electric field
Scientific Reports (2024)
-
Interplay between hopping dimerization and quasi-periodicity on flux-driven circular current in an incommensurate Su–Schrieffer–Heeger ring
Scientific Reports (2023)
-
Correlated disorder as a way towards robust superconductivity
Communications Physics (2022)
-
Detrended fluctuation analysis of seismicity and order parameter fluctuations before the M7.1 Ridgecrest earthquake
Natural Hazards (2020)
-
Effect of short-ranged spatial correlations on the Anderson localization of phonons in mass-disordered systems
Bulletin of Materials Science (2020)
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.