Disorder effects on the charge-density waves structure in V- and W-doped blue bronzes: Friedel oscillations and charge-density wave pinning

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 17, 2006, Pages

  Ravy, S ^a   Rouziere S ^b   Pouget, J P ^b   Brazovskii, S ^c   Marcus, J ^d   Berar J F ^d   Elkaim, E ^a  

^a SYNCHROTRON SOLEIL   (France)

^b UNIVERSITÉ PARIS SUD   (France)

^c UNIVERSITÉ PARIS SUD   (France)

^d LABORATOIRE DE CRISTALLOGRAPHIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750583116     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.174102     Document Type: Article

References (88)

1. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
2. N. F. Mott and W. D. Twose, Adv. Phys. ADPHAH 0001-8732 10.1080/00018736100101271 10, 107 (1961).
3. R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York, 1955).
4. H. Frohlich, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 223, 296 (1954);
5. D. Allender, J. W. Bray, and J. Bardeen, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.9.119 9, 119 (1974).
6. P. Monceau, N. P. Ong, A. M. Portis, A. Meerschaut, and J. Rouxel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.37.602 37, 602 (1976).
7. Low Dimensional Properties of Quasi-One-Dimensional Materials, edited by, P. Monceau, (Reidel, Dordrecht, 1985).
8. G. Grüner, Density Waves in Solids, Frontiers in Physics Vol. 89 (Addison-Wesley, Reading, MA, 1994).
9. Physics and Chemistry of Low Dimensional Inorganic Conductors, Vol. 354 of NATO Advanced Study Institute, Series B: Physics, edited by, C. Schlenker,,, J. Dumas,,, M. Greenblatt,, and, S. Van Smaalen, (Plenum, New York, 1996).
10. A. I. Larkin, Sov. Phys. JETP SPHJAR 0038-5646 31, 784 (1970).
11. A. I. Larkin and Yu. N. Ovchinnikov, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00117160 34, 409 (1979).
12. H. Fukuyama and P. A. Lee, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.17.535 17, 535 (1978).
13. P. A. Lee and T. M. Rice, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.19.3970 19, 3970 (1979).
14. For a review on CDW pinning, see, e.g., S. Brazovskii and T. Nattermann, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730410001684197 53, 177 (2004).
15. D. A. DiCarlo, J. McCarten, T. L. Adelman, M. Maher, and R. E. Thorne, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.7643 42, 7643 (1990);
16. J. McCarten, D. A. DiCarlo, M. P. Maher, T. L. Adelman, and R. E. Thorne, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.4456 46, 4456 (1992).
17. J. R. Tucker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.7614 47, 7614 (1993).
18. Y. Imry and S. Ma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 35.1399 35, 1399 (1975).
19. S. Abe, J. Phys. Soc. Jpn. JUPSAU 0031-9015 54, 3498 (1985);
20. S. Abe, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.55.1987 55, 1987 (1986).
21. I. Bĝldea, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.51.1495 51, 1495 (1995);
22. I. Bĝldea, H. Köppel, and L. S. Cederbaum, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.11845 52, 11845 (1995).
23. A. I. Larkin and S. Brazovskii, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(94)00749-7 93, 275 (1995).
24. I. Tütto and A. Zawadowski, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.32.2449 32, 2449 (1985).
25. S. Rouzière, S. Ravy, S. Brazovskii, and J.-P. Pouget, J. Phys. IV JPICEI 1155-4339 9, Pr10-23 (1999).
26. S. Rouzière, S. Ravy, J.-P. Pouget, and S. Brazovskii, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.62.R16231 62, R16231 (2000).
27. S. Ravy, S. Rouzière, E. Elkaim, J.-P. Pouget, and S. Brazovskii, J. Phys. IV JPICEI 1155-4339 12, Pr9-79 (2002).
28. A. Rosso and T. Giamarchi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.140201 68, 140201 (R) (2003).
29. A. Rosso and T. Giamarchi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.224204 70, 224204 (2004).
30. L. Forro, L. Zuppiroli, J. P. Pouget, and K. Bechgaard, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.27.7600 27, 7600 (1983);
31. L. Forro, S. Bouffard, and J. P. Pouget, J. Phys. (France) Lett. JPSLBO 0302-072X 45, L543 (1984).
32. S. Girault, A. H. Moudden, J.-P. Pouget, and J.-M. Godard, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.7980 38, 7980 (1988).
33. S. M. DeLand, G. Mozurkewich, and L. D. Chapman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.2026 66, 2026 (1991).
34. E. Sweetland, C-Y. Tsai, B. A. Wintner, J. D. Brock, and R. E. Thorne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.3165 65, 3165 (1990).
35. J. D. Brock, A. C. Finnefrock, K. L. Ringland, and E. Sweetland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3588 73, 3588 (1994).
36. D. DiCarlo, R. E. Thorne, E. Sweetland, M. Sutton, and J. D. Brock, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.8288 50, 8288 (1994).
37. S. Rouzière, S. Ravy, J.-P. Pouget, and R. E. Thorne, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.15121 59, 15121 (1999).
38. S. Rouzière, S. Ravy, and J.-P. Pouget, Synth. Met. SYMEDZ 0379-6779 10.1016/0379-6779(94)02844-O 70, 1259 (1995).
39. S. Ravy, J.-P. Pouget, and R. Comès, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1992203 2, 1173 (1992).
40. S. Ravy and J.-P. Pouget, J. Phys. IV JPICEI 1155-4339 3, C2-109 (1993).
41. S. Brazovskii, J.-P. Pouget, S. Ravy, and S. Rouzière, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.3426 55, 3426 (1997).
42. M. A. Krivoglaz, Theory of X-ray and Thermal Neutrons Scattering by Real Crystals (Plenum, New York, 1969).
43. J. P. Pouget, in Semi-conductors and Semi-metals, edited by, E. M. Conwell, (Academic, New York, 1988), Vol. 27, p. 87.
44. L. J. Sham, in Highly Conducting One-dimensional Solids, edited by, J. J. Devrese,,, R. P. Evrard,, and, V. E. van Doren, (Plenum, New York, 1979), Chap., p. 227.
45. K. B. Efetov and A. I. Larkin, Sov. Phys. JETP SPHJAR 0038-5646 72, 2350 (1977).
46. K. B. Efetov and A. I. Larkin, Sov. Phys. JETP SPHJAR 0038-5646 [Sov. Phys. JETP SPHJAR 0038-5646 45, 1236 (1977)].
47. T. Nattermann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64. 2454 64, 2454 (1990).
48. S. E. Korshunov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.3969 48, 3969 (1993).
49. T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1530 72, 1530 (1994);
50. T. Giamarchi, and P. Le Doussal, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.52.1242 52, 1242 (1995).
51. D. Feinberg and J. Friedel, in Low-Dimensional Electronic Properties of Molybdenum Bronzes and Oxides, edited by, C. Schlenker, (Kluwer Academic, Dordrecht, 1989), p. 407.
52. P. Debye, H. R. Anderson, Jr., and H. Brumberger, J. Appl. Phys. JAPIAU 0021-8979 38, 679 (1957).
53. D. Le Bolloc'h, S. Ravy, J. Dumas, J. Marcus, F. Livet, C. Detlefs, F. Yakhou, and L. Paolasini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 95.116401 95, 116401 (2005).
54. Interestingly enough, the surface scattering by an array of CDW dislocations has been shown to yield PA: see N. Kirova and S. Brazovskii, J. Phys. IV JPICEI 1155-4339 131, 147 (2005).
55. J. M. Cowley, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(93)90046-M 298, 336 (1993).
56. T. R. Welberry and N. J. Fox, J. Appl. Crystallogr. JACGAR 0021-8898 28, 611 (1995).
57. S. Barišić and I. Batistic, J. Phys. (France) JOPQAG 0302-0738 50, 2717 (1989).
58. S. Ravy, J. Phys. IV JPICEI 1155-4339 12, Pr6-7 (2002).
59. B. E. Warren, X-ray Diffraction (Addison-Wesley, Reading, MA, 1969).
60. J. Graham and A. D. Wadsley, Acta Crystallogr. ACCRA9 0365-110X 10.1107/S0365110X66000173 20, 93 (1966).
61. M. H. Whangbo and L. F. Schneemeyer, Inorg. Chem. INOCAJ 0020-1669 10.1021/ic00234a028 25, 2424 (1986).
62. J.-L. Mozos, P. Ordejon, and E. Canadell, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.233105 65, 233105 (2002).
63. J.-P. Pouget, S. Kagoshima, C. Schlenker, and J. Marcus, J. Phys. (France) Lett. JPSLBO 0302-072X 44, L113 (1983).
64. J.-P. Pouget, C. Noguera, A. H. Moudden, and R. Moret, J. Phys. (France) JOPQAG 0302-0738 46, 1731 (1985).
65. W. J. Schutte and J. L. De Boer, Acta Crystallogr., Sect. B: Struct. Sci. ASBSDK 0108-7681 10.1107/S0108768188007001 44, 486 (1988).
66. G. V. Samsonov, Handbook of the Physicochemical Properties of the Elements (Plenum, New York 1968).
67. S. Girault, thesis, Université d'Orsay (1987).
68. J. Dumas, B. Laayadi, and R. Buder, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.2968 40, 2968 (1989).
69. L. Degiorgi, B. Alavi, G. Mihaly, and G. Gruner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.7808 44, 7808 (1991);
70. L. Degiorgi and G. Gruner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.7820 44, 7820 (1991).
71. T. Tamegai, K. Tsutsumi, and S. Kagoshima, Synth. Met. SYMEDZ 0379-6779 10.1016/0379-6779(87)90477-2 19, 923 (1987).
72. L. F. Schneemeyer, F. J. DiSalvo, S. E. Spengler, and J. V. Waszczak, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.30.4297 30, 4297 (1984).
73. L. F. Schneemeyer, R. M. Fleming, and S. E. Spengler, Solid State Commun. SSCOA4 0038-1098 53, 505 (1985).
74. J. Dumas, C. Schlenker, J. Marcus, and R. Buder, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.757 50, 757 (1983).
75. E. Orignac, A. Rosso, R. Chitra, and T. Giamarchi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.035112 73, 035112 (2006).
76. S. Girault, A. H. Moudden, and J.-P. Pouget, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.4430 39, 4430 (1989).
77. J. M. Ziman, Principle of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, UK, 1972). In 1D, where the Fermi surface consists of two points at ± kF, only the l=0 term has to be considered in the expression (5.43).
78. J. Friedel in Electron-phonon Interactions and Phase Transitions, edited by, T. Riste, (Plenum, New York, 1977).
79. For the sake of consistency, let us recall that for a semiconductor one has [see N. Bloembergen and T. J. Rowland, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.97.1679 97, 1679 (1955)] ξΔ = 2 meff Eg, which gives ξΔ = vF Eg by taking the effective mass of the Peierls insulating ground state meff = Δ0 vF2. Note that the damping length ξΔ is twice as small as the classical coherence length ξ0 = vF Δ0. In this paper, we prefer to use ξΔ because it directly enters the exponential decay of the s [Eq. 31].
80. G.-H. Gweon, J. W. Allen, R. Claessen, J. A. Clack, D. M. Poirier, P. J. Benning, C. G. Olson, W. P. Ellis, Y.-X. Zhang, L. F. Schneemeyer, J. Marcus, and C. Schlenker, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/8/48/017 8, 9923 (1996).
81. A. Guinier, X-ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, New York, 1994).
82. J.-P. Pouget, S. Ravy, S. Rouzière, and S. Brazovskii, J. Phys. IV JPICEI 1155-4339 12, Pr9-9 (2002).
83. J. P. Pouget, in Low-Dimensional Electronic Properties of Molybdenum Bronzes and Oxides, edited by, C. Schlenker, (Kluwer Academic Publishers, Dordrecht, 1989), p. 87.
84. T. Giamarchi and P. Le Doussal, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.6577 55, 6577 (1997).
85. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965).
86. B. Hennion, J.-P. Pouget, and M. Sato, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2374 68, 2374 (1992);
87. J.-P. Pouget, B. Hennion, C. Escribe-Filippini, and M. Sato, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.8421 43, 8421 (1991).
88. J. Odin, J. C. Lasjaunias, K. Biljakovic, K. Hasselbach, and P. Monceau, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s10051-001-8680-7 24, 315 (2001).