Electronic transport properties of quasicrystals

Journal of Mathematical Physics

Volumn 38, Issue 4, 1997, Pages 1794-1822

  Roche, S ^a,b   De Laissardière, G Trambly ^a,c   Mayou, D ^a  

^a LABORATOIRE DE CRISTALLOGRAPHIE   (France)

^b UNIVERSITY OF TOKYO   (Japan)

^c CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345791559     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531914     Document Type: Article

References (104)

1. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 51, 1951 (1984).
2. H. Bohr and H. Cohn, Almost Periodic Functions (Chelsea, New York, 1947).
3. Quasicrystals, The State of the Art, edited by D. P. DiVicenzo and P. J. Steinhardt (World Scientific, Singapore, 1991), Vol. 11.
4. L. Pauling, Phys. Rev. Lett. 58, 365 (1987).
5. A. P. Tsai, A. Inoue, and T. Masumoto, Jpn. J. Appl. Phys. 26, L1505 (1987); A. P. Tsai, A. Inoue, and T. Masumoto, Mat. Trans. JIM 31, 98 (1990).
6. A. P. Tsai, A. Inoue, and T. Masumoto, Jpn. J. Appl. Phys. 26, L1505 (1987); A. P. Tsai, A. Inoue, and T. Masumoto, Mat. Trans. JIM 31, 98 (1990).
7. Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995).
8. M. Duneau, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994), Chap. 2.
9. R. Penrose, Bull. Inst. Math. Appl. 10, 226 ( 1974).
10. C. Janot, Quasicrystals: A Primer (Clarendon, Oxford, 1992).
11. N. G. De Brujin, Nederl. Akad. Wetensch. Proc. Ser. A 43, 39 (1981).
12. M. Duneau and A. Katz, Phys. Rev. Lett. 54, 2688 (1985).
13. S. Katz and D. Gratias, Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994).
14. N. D. Mermin, in Quasicrystals, The State of the Art, edited by D. P, DiVicenzo and P. J. Steinhardt (World Scientific, Singapore, 1991), Vol. 11.
15. C. Janot and M. de Boissieu, Phys. Rev. Lett. 72, 1674 (1994); C. Janot, Phys. Rev. B 53, 181 (1996).
16. C. Janot and M. de Boissieu, Phys. Rev. Lett. 72, 1674 (1994); C. Janot, Phys. Rev. B 53, 181 (1996).
17. M. Cornier-Quiquandon, M. Quivy, S. Lefebvre, E. Elkaim, G. Heger, A. Katz, and D. Gratias, Phys. Rev. B 44, 2071 (1991).
18. M. Boudard, M. de Boissieu, C. Janot, J. M. Dubois, and C. Dong, Philos. Mag. Lett. 64, 197 (1991).
19. M. Boudard et al., J. Phys. Condens. Matter 4, 10 149 (1992).
20. S. Martin, A. F. Hebard, A. R. Kortan, and F. A. Thiel, Phys. Rev. Lett. 67, 719 (1991).
21. T. Klein, Ph.D. thesis, University of Joseph-Fourier, 1992.
22. D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, Phys. Rev. Lett. 70, 3915 (1993).
23. S. J. Poon, F. S. Pierce, Q. Guo, and P. Volkov, Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995), p. 408.
24. C. Berger, C. Gignoux, T. Wagner, T. Grenet, G. Fourcaudot, J. L. Grieco, Y. Calvayrac, and J. L. Lasjaunias, Proceedings of the Ninth International Conference on Rapidly Quenched in Metastable Materials RQ9, Août, 1996 (unpublished); C. Berger, T. Wagner, G. Fourcaudot, and Y. Calvayrac (unpublished).
25. B. D. Biggs, F. S. Pierce, and S. J. Poon, Europhys. Lett. 1992, 415 (1992); K. Edagawa, N. Naito, and T. Takeuchi, Philos. Mag. B 65, 1011 (1993).
26. B. D. Biggs, F. S. Pierce, and S. J. Poon, Europhys. Lett. 1992, 415 (1992); K. Edagawa, N. Naito, and T. Takeuchi, Philos. Mag. B 65, 1011 (1993).
27. C. Gignoux, Ph.D. thesis in preparation, University of Joseph-Fourier, 1996; C. Gignoux and G. Berger (unpublished).
28. C. Gignoux, Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995).
29. F. S. Pierce, Q. Guo, and S. J. Poon, Phys. Rev. Lett. 73, 2220 (1994).
30. N. Mott, Metal-Insulator Transition, 2nd ed. (Taylor & Francis, London, 1990).
31. C. Berger, Seminar 3, Les Houches, edited by E. Akkermans, G. Montambaux, J. L. Pichard, and J. Zinn-Justin (Elsevier, North Holland, Amsterdam, 1995), Session LXI.
32. Y. Honda, K. Edagawa, A. Yoshioka, T. Hashimoto, and S. Takeuchi, Jpn. J. Appl. Phys. 33, 1929 (1994).
33. S. Takeuchi, H. Akiyama, N. Naito, T. Shibuya, and T. Hashimoto, J. Non-Cryst. Solids 153/154, 353 (1993).
34. B. D. Biggs, S. J. Poon, and N. Munirathnan, Phys. Rev. Lett. 65, 2700 (1990); S. J. Poon, Adv. Phys. 41, 303 (1992).
35. B. D. Biggs, S. J. Poon, and N. Munirathnan, Phys. Rev. Lett. 65, 2700 (1990); S. J. Poon, Adv. Phys. 41, 303 (1992).
36. P. Lidquist, P. Canco, C. Berger, A. G. M. Jansen, and F. Gyrot-Lockmann, Phys. Rev. B 51, 4796 (1995).
37. C. Berger (private communication).
38. D. Mayou, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Éditions de Physique, Les Ulis, 1994).
39. C. Berger, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994).
40. M. Kohmoto, L. P. Kadanoff, and Ch. Tang, Phys. Rev. Lett. 50, 1870 (1983); S. Ostlund, R. Petit, D. Ret, H. J. Schellnhuber, and E. D. Siggia, ibid. 50, 1873 (1983).
41. M. Kohmoto, L. P. Kadanoff, and Ch. Tang, Phys. Rev. Lett. 50, 1870 (1983); S. Ostlund, R. Petit, D. Ret, H. J. Schellnhuber, and E. D. Siggia, ibid. 50, 1873 (1983).
42. M. Kohmoto, Int. J. Mod. Phys. B 1, 31 (1986).
43. M. Kohmoto and J. R. Banavar, Phys. Rev. B 34, 563 (1986).
44. H. Hentschel and I. Procaccia, Physica D 8, 435 (1983).
45. H. Kubo and M. Goda, J. Phys. Soc. Jpn. 62, 2601 (1993).
46. T. Fujiwara, in Solid-State Science 93 Quasicrystals, edited by Fujiwara and Ogawa (Springer-Verlag, Berlin, 1990).
47. J. Bellissard, B. Iochum, and D. Testard, Commun. Math. Phys. 141, 353 (1991).
48. J. Bellissard, in From Number Theory to Physics, edited by M. Waldschmidt, P. Moussa, J. Luck, and C. Itzykson (Springer, Berlin, 1991).
49. C. Sire and R. Mosseri, J. Phys. (Paris) 50, 3447 (1989).
50. C. Sire, B. Passaro, and V. G. Benza, J. Non-Cryst. Solids 153&154, 420 (1993).
51. T. Fujiwara and H. Tsunetsugu, Quasicrystals: The States of the Art. edited by D. P. Di Vincenzo and P. J. Steinhart (World Scientific, Singapore, 1991), p. 343.
52. S. Yamamoto and T. Fujiwara, Phys. Rev. B 51, 8841 (1995).
53. T. Fujiwara (private communication).
54. C. Sire, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994); Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995).
55. C. Sire, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994); Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995).
56. H. Hiramoto and S. Abe, J. Phys. Soc. Jpn. 57, 230 (1988).
57. F. Piéchon, Phys. Rev. Lett. 76, 4372 (1996).
58. G. Jona-Lasinio, F. Martinelli, and E. Scoppola, J. Phys. A 17, L635 (1984); ibid. Ann. Inst. Henri Poincaré 42, 73 (1985).
59. G. Jona-Lasinio, F. Martinelli, and E. Scoppola, J. Phys. A 17, L635 (1984); ibid. Ann. Inst. Henri Poincaré 42, 73 (1985).
60. M. Kohmoto, Phys. Rev. B 34, 5043 (1986); B. Sutherland and M. Kohmoto, ibid. 36, 5877 (1987).
61. M. Kohmoto, Phys. Rev. B 34, 5043 (1986); B. Sutherland and M. Kohmoto, ibid. 36, 5877 (1987).
62. B. Iochum and D. Testard, J. Stat. Phys. 65, 715 ( 1991); B. Iochum, L. Raymond, and D. Testard, Physica A 187, 353 (1992).
63. B. Iochum and D. Testard, J. Stat. Phys. 65, 715 ( 1991); B. Iochum, L. Raymond, and D. Testard, Physica A 187, 353 (1992).
64. H. Tsunutsegu and K. Ueda, Phys. Rev. B 43, 8892 (1991).
65. T. Fujiwara, Phys. Rev. B 40, 942 (1992); T. Fujiwara and T. Yokokawa, Phys. Rev. Lett. 66, 333 (1991).
66. T. Fujiwara, Phys. Rev. B 40, 942 (1992); T. Fujiwara and T. Yokokawa, Phys. Rev. Lett. 66, 333 (1991).
67. T. Fujiwara, S. Yamamoto, and G. Trambly de Laissardiere, Phys. Rev. Lett. 71, 4166 (1993).
68. G. Trambly de Laissardière, Ph.D. thesis, University of Joseph-Fourier, 1996.
69. E. Belin, Z. Dankházi, A. Sadoc, and J. M. Dubois, Europhys. Lett. 26, 677 (1992).
70. B. D. Biggs, S. J. Poon, and N. R. Munirathnam, Phys. Rev. Lett. 65, 2700 (1990).
71. F. Hippert, L. Ketel, Y. Calvayrac, and B. Dubost, Phys. Rev. Lett. 69, 2086 (1992); E. Belin, Z. Dankhzi, A. Sadoc, and J.-M. Dubois, Europhys. Lett. 26, 677 (1994); E. Belin, Z. Dankhzi, and A. Sadoc, Mater. Sci. Eng. A 181/182, 717 (1994).
72. F. Hippert, L. Ketel, Y. Calvayrac, and B. Dubost, Phys. Rev. Lett. 69, 2086 (1992); E. Belin, Z. Dankhzi, A. Sadoc, and J.-M. Dubois, Europhys. Lett. 26, 677 (1994); E. Belin, Z. Dankhzi, and A. Sadoc, Mater. Sci. Eng. A 181/182, 717 (1994).
73. F. Hippert, L. Ketel, Y. Calvayrac, and B. Dubost, Phys. Rev. Lett. 69, 2086 (1992); E. Belin, Z. Dankhzi, A. Sadoc, and J.-M. Dubois, Europhys. Lett. 26, 677 (1994); E. Belin, Z. Dankhzi, and A. Sadoc, Mater. Sci. Eng. A 181/182, 717 (1994).
74. W. Hume-Rothery, J. Inst. Met. 35, 295 (1926); W. Hume-Rothery and G. V. Raynor, The Structure of Metals and Alloys (Institute of Metals, London, 1954).
75. W. Hume-Rothery, J. Inst. Met. 35, 295 (1926); W. Hume-Rothery and G. V. Raynor, The Structure of Metals and Alloys (Institute of Metals, London, 1954).
76. J. Friedel, Philos. Mag. 43, 153 (1952); J. Phys. Radium 23, 692 (1962); J. Phys. Can. 34, 1190 (1956).
77. J. Friedel, Philos. Mag. 43, 153 (1952); J. Phys. Radium 23, 692 (1962); J. Phys. Can. 34, 1190 (1956).
78. J. Friedel, Philos. Mag. 43, 153 (1952); J. Phys. Radium 23, 692 (1962); J. Phys. Can. 34, 1190 (1956).
79. J. Friedel and F. Dénoyer, C. R. Acad. Sci. Paris 305, 171 (1987).
80. H. Jones, Proc. Phys. Soc. 49, 250 (1937); H. Jones, J. Phys. Radium 23, 637 (1996).
81. H. Jones, Proc. Phys. Soc. 49, 250 (1937); H. Jones, J. Phys. Radium 23, 637 (1996).
82. T. Fujiwara, T. Mitsui, and S. Yamamoto, Phys. Rev. B 53, R2910 (1996).
83. S. E. Burkov, T. Timusk, and N. W. Ashcroft, J. Phys. C 4, 9447 (1992).
84. G. Trambly de Laissardière, S. Roche, and D. Mayou, Proceedings of the Ninth International Conference on Rapidly Quenched in Metastable Materials RQ9, Août, 1996 (unpublished).
85. G. Trambly de Laissardière and D. Mayou, Phys. Rev. B (to be published).
86. D. N. Davydov, D. Mayou, C. Berger, C. Gignoux, A. Neumann, A. G. M. Jansen, and P. Wyder, Phys. Rev. Lett. 77, 3173 (1996).
87. E. Belin and D. Mayou, Phys. Scr. T 49, 356 (1993).
88. V. G. Benza and C. Sire, Phys. Rev. B 44, 10 343 (1991); B. Passaro, C. Sire, and V. G. Benza, ibid. 46, 13 751 (1992); C. Sire, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994).
89. V. G. Benza and C. Sire, Phys. Rev. B 44, 10 343 (1991); B. Passaro, C. Sire, and V. G. Benza, ibid. 46, 13 751 (1992); C. Sire, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994).
90. V. G. Benza and C. Sire, Phys. Rev. B 44, 10 343 (1991); B. Passaro, C. Sire, and V. G. Benza, ibid. 46, 13 751 (1992); C. Sire, in Lectures on Quasicrystals, edited by F. Hippert and D. Gratias (Les Editions de Physique, Les Ulis, 1994).
91. J. Bellissard, A. van Elst, and H. Schultz-Baldes. J. Math. Phys. 35, 5373 (1994); J. Bellissard and H. Schulz-Baldes, in Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995); J. Bellissard and H. Schulz-Baldes, preprint (1996).
92. J. Bellissard, A. van Elst, and H. Schultz-Baldes. J. Math. Phys. 35, 5373 (1994); J. Bellissard and H. Schulz-Baldes, in Proceedings of the 5th International Conference on Quasicrystals, edited by C. Janot and R. Mosseri (World Scientific, Singapore, 1995); J. Bellissard and H. Schulz-Baldes, preprint (1996).
93. K. Moulopoulos and S. Roche, Phys. Rev. B 53, 212 (1996); S. Roche (in preparation).
94. K. Moulopoulos and S. Roche, J. Condens. Matter 7. 8883 (1995).
95. M. T. Béal-Monod and G. Forgacs, Phys. Rev. B 37, 6646 (1988).
96. Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam, 1991).
97. M. B. Hastings, A. D. Stone, and H. U. Baranger, Phys. Rev. B 50, 8230 (1994); H. U. Baranger, R. A. Jalabert, and A. D. Stone, Phys. Rev. Lett. 70, 3876 (1993); Chaos 3, 665 (1988).
98. M. B. Hastings, A. D. Stone, and H. U. Baranger, Phys. Rev. B 50, 8230 (1994); H. U. Baranger, R. A. Jalabert, and A. D. Stone, Phys. Rev. Lett. 70, 3876 (1993); Chaos 3, 665 (1988).
99. M. B. Hastings, A. D. Stone, and H. U. Baranger, Phys. Rev. B 50, 8230 (1994); H. U. Baranger, R. A. Jalabert, and A. D. Stone, Phys. Rev. Lett. 70, 3876 (1993); Chaos 3, 665 (1988).
100. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
101. D. A. Greenwood, Proc. Phys. Soc. London 71, 585 (1958).
102. S. Roche, Ph.D. thesis, 1996.
103. S. Roche and D. Mayou (unpublished).
104. D. Mayou et al. (unpublished).