Abstract
Quasicrystals are metallic alloys that possess perfect long-range structural order, in spite of the fact that their rotational symmetries are incompatible with long-range periodicity. The exotic structural properties of this class of materials1 are accompanied by physical properties that are unexpected for metallic alloys. Considerable progress in resolving the geometric structures of quasicrystals has been made using X-ray and neutron diffraction, and concepts such as the quasi-unit-cell model2 have provided theoretical insights. But the basic properties of the valence electronic states—whether they are extended as in periodic crystals or localized as in amorphous materials—are still largely unresolved3. Here we investigate the electronic bandstructure of quasicrystals through angle-resolved photoemission experiments on decagonal Al71.8Ni14.8Co13.4. We find that the s-p and d states exhibit band-like behaviour with the symmetry of the quasiperiodic lattice, and that the Fermi level is crossed by dispersing d-bands. The observation of free-electron-like bands, distributed in momentum space according to the surface diffraction pattern, suggests that the electronic states are not dominated by localization.
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
Schechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984).
Steinhardt, P. J. et al. Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature 396, 55–57 (1998); correction Nature 399, 84 (1999).
Janot, C. Quasicrystals: A Primer 359–399 (Oxford Univ. Press, New York, 1997).
Hafner, J. & Krajci, M. in Physical Properties of Quasicrystals (ed. Stadnik, Z. M.) (Springer, Berlin, 1999).
Smith, A. P. & Ashcroft, N. W. Pseudopotentials and quasicrystals. Phys. Rev. Lett. 59, 1365– 1368 (1987).
Niizeki, K. & Akamatsu, T. Special points in the reciprocal space of an icosahedral quasi-lattice and the quasi-dispersion relation of electrons. J. Phys. Cond. Mat. 2, 2759– 2771 (1990).
Trambly de Laissardiere, G. & Mayou, D. Clusters and localization of electrons in quasicrystals. Phys. Rev. B 55, 2890–2893 (1997).
Rapp, Ö. in Physical Properties of Quasicrystals (ed. Stadnik, Z. M.) 127– 167 (Springer, Berlin, 1999).
Kevan, S. D. (ed.) Angle Resolved Photoemission (Elsevier, Amsterdam, 1992).
Wu, X. et al. Electronic band dispersion and pseudogap in quasicrystals-angular-resolved photoemission studies on icosahedral Al70Pd21.5Mn 8.5. Phys. Rev. Lett. 75, 4540– 4543 (1995).
Gille, P., Dreier, P., Gräber, M. & Scholpp, T. Large single-grain AlCoNi quasicrystals grown by the Czochralski method. J. Cryst. Growth 207, 95–101 (1999).
Zurkirch, M., Bolliger, B., Erbudak, M. & Kortan, A. R. Structural transformations at the surface of the decagonal quasicrystal Al 70Co15Ni15. Phys. Rev. B 58, 14113–14116 (1998).
Rotenberg, E. & Kevan, S. D. Evolution of Fermi level crossings versus H coverage on W(110). Phys. Rev. Lett. 80, 2905–2908 (1998).
Osterwalder, J., Greber, T., Hüfner, S. & Schlapbach, L. X-ray-photoelectron diffraction from a free-electron-metal valence band: evidence for hole-state localization. Phys. Rev. Lett. 64, 2683–2686 (1990).
Roche, S. & Fujiwara, T. Fermi surfaces and anomalous transport in quasicrystals. Phys. Rev. B 58, 11338 –11343 (1998).
Senechal, M. Quasicrystals and Geometry (Cambridge Univ. Press, Cambridge, 1995).
Steurer, W., Haibach, T., Zhang, B., Kek, S. & Lück, R. The structure of decagonal Al70Ni15 Co15. Acta Crystallogr. B 49, 661–675 (1993).
Fujiwara, T., Kohmoto, M. & Tokihiro, T. Multifractal wave functions on a Fibonacci lattice. Phys. Rev. B 40, 7413– 7416 (1989).
Gardner, M. Extraordinary nonperiodic tiling that enriches the theory of tiles. Sci. Am. 236, 110–117 ( 1977).
Acknowledgements
This work is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy at Lawrence Berkeley National Laboratory. P.G. and W.T. acknowledge support from the Deutsche Forschungsgemeinschaft.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rotenberg, E., Theis, W., Horn, K. et al. Quasicrystalline valence bands in decagonal AlNiCo. Nature 406, 602–605 (2000). https://doi.org/10.1038/35020519
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/35020519
This article is cited by
-
Fermi states and anisotropy of Brillouin zone scattering in the decagonal Al–Ni–Co quasicrystal
Nature Communications (2015)
-
Anomalous transport of light in photonic crystal
Science China Information Sciences (2013)
-
Strongly linearly polarized low threshold lasing of all organic photonic quasicrystals
Scientific Reports (2012)
-
Wave and defect dynamics in nonlinear photonic quasicrystals
Nature (2006)
-
Negative refraction and focusing of electromagnetic wave through two-dimensional photonic crystals
Frontiers of Physics in China (2006)
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.