Publication: Suppression of localization in kronig-penney models with correlated disorder
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1994-01-01
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American Physical Society
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Abstract
We consider the electron dynamics and transport properties of one-dimensional continuous models with random, short-range correlated impurities. We develop a generalized Poincare map formalism to cast the Schrodinger equation for any potential into a discrete set of equations, illustrating its application by means of a specific example. We then concentrate on the case of a Kronig-Penney model with dimer impurities. The previous technique allows us to show that this model presents infinitely many resonances (zeroes of the reflection coefficient at a single dimer) that give rise to a band of extended states, in contradiction with the general viewpoint that all one-dimensional models with random potentials support only localized states. We report on exact transfer-matrix numerical calculations of the transmission coefFicient, density of states, and localization length for various strengths of disorder. The most important conclusion so obtained is that this kind of system has a very large number of extended states. Multifractal analysis of very long systems clearly demonstrates the extended character of such states in the thermodynamic limit. In closing, we brieBy discuss the relevance of these results in several physical contexts.
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© 1994 The American Physical Society.
Thanks are warmly due to Rainer Scharf, who introduced us to the topic of the random dimer model and the suppresion of localization. All computations have been
carried out using facilities of the Universidad Carlos III de Madrid. A.S. acknowledges partial support from CICyT (Spain) through Project No. PB92-0248.
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1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
2. P. Dean, Proc. Phys. Soc. 84, 727 (1964).
3. J. M. Ziman, Modele of Disorder (Cambridge University Press, London, 1979).
4. Fluctuations and Order: The NewSynthesis, edited by M. M. Millonas (MIT Press, Boston, MA, in press).
5. R. Bourbonnais and R. Maynard, Phys. Rev. Lett. 64, 1397 (1990); Yu. S. Kivshar, S. A. Gredeskul, A. Sánchez, and L. Vázquez, ibid. 64, 1693 (1990).
6. A. Sánchez and L. Vázquez, Int. J. Mod. Phys. B 5, 2825 (1991); S. A. Gredeskul and Yu. S. Kivshar, Phys. Rep. 218, 1 (1992).
7. D. H. Dunlap, H.-L. Wu, and P. Phillips, Phys. Rev. Lett. 65, 88 (1990).
8. H.-L. Wu and P. Phillips, J. Chem. Phys. 93, 7369 (1990).
9. H.-L. Wu and P. Phillips, Phys. Rev. Lett. 66, 1366 (1991).
10. P. Phillips and H.-L. Wu, Science 252, 1805 (1991).
11. J. C. Flores, J. Phys. Condens. Matter 1, 8471 (1989).
12. A. Bovier, J. Phys. A 25, 1021 (1992).
13. S. Gangopadhyay and A. K. Sen, J. Phys. Condens. Matter 4, 9939 (1992).
14. P. K. Datta, D. Giri, and K. Kundu, Phys. Rev. B 47, 10 727 (1993).
15. H.-L. Wu, W. GoK, and P. Phillips, Phys. Rev. B 45, 1623 (1992).
16. S. N. Hvangelou, and A. Z. Wang, Phys. Rev. B 47, 13 126 (1993).
17. S. N. Evangelou and D. E. Katsanos, Phys. Lett. A 164, 456 (1992).
18. F. Domínguez-Adame, E. Maciá, and A. Sánchez, Phys. Rev. B 48, 6054 (1993).
19. R. de L. Kronig and W. G. Penney, Proc. R. Soc. London, Ser. A 130, 499 (1931).
20. See, e.g., E. Lieb and D. C. Mattis, Mathematica/Physics in One Dimension (Academic Press, New York, 1966).
21. M. Jaros, Physics and Apptication of Semiconductor Microstructures (Clarendon Press, Oxford, 1989).
22. E. Tuncel and L. Pavesi, Philos. Mag. B 65, 213 (1992).
23. Y. Tanaka and M. Tsukada, Phys. Rev. B 40, 4482 (1989).
24. G. J. Clerk and B. H. J. McKellar, Phys. Rev. C 41, 1198 (1990).
25. P. Erdos and R. C. Herndon, Helv. Phys. Acta 50, 513 (1977).
26. M. Schreiber and H. Grussbach, Mod. Phys. Lett. B B, 851 (1992).
27. M. Kohmoto, Phys. Rev. B 34, 5043 (1986).
28. J. Bellissard, A. Formoso, R. Lima, and D. Testard, Phys. Rev. B 26, 3024 (1982).
29. J. B. Sokoloff and J. V. Jose, Phys. Rev. Lett. 49, 334 (1982).
30. P. D. Kirkman and J. B. Pendry, 3. Phys. C 17, 4327 (1984).
31. R. Landauer, Philos. Mag. 21, 863 (1970).
32. J. Canisius and J. L. van Hemmen, J. Phys. C 18, 4873 (1985).
33. J. Sun, Phys. Rev. B 40, 8270 (1989).
34. F. Domínguez-Adame and A. Sánchez, Phys. Lett. A 159, 153 (1991).