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Journal of Low Temperature Physics

, Volume 150, Issue 1–2, pp 57–81 | Cite as

Response, Relaxation and Transport in Unconventional Superconductors

  • Dietrich Einzel
  • Ludwig Klam
Article

Abstract

We investigate the collision-limited electronic Raman response and the attenuation of ultrasound in spin-singlet d-wave superconductors at low temperatures. The dominating elastic collisions are treated within a t-matrix approximation, which combines the description of weak (Born) and strong (unitary) impurity scattering. In the long wavelength limit a two-fluid description of both response and transport emerges. Collisions are here seen to exclusively dominate the relaxational dynamics of the (Bogoliubov) quasiparticle system and the analysis allows for a clear connection of response and transport phenomena. When applied to quasi-2-d superconductors like the cuprates, it turns out that the transport parameter associated with the Raman scattering intensity for B1g and B2g photon polarization is closely related to the corresponding components of the shear viscosity tensor, which dominates the attenuation of ultrasound. At low temperatures we present analytic solutions of the transport equations, resulting in a non-power-law behavior of the transport parameters on temperature.

Keywords

Unconventional superconductivity Two-fluid description Transport and electronic Raman effect Ultrasound attenuation 

PACS

67.57.Hi 74.20.-z 74.20.Fg 74.20.Rp 74.25.Fy 74.25.Ld 

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References

  1. 1.
    D.D. Osheroff, D.M. Lee, R.C. Richardson, Phys. Rev. Lett. 29, 920 (1972) CrossRefADSGoogle Scholar
  2. 2.
    For a theoretical review see: A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975) CrossRefADSGoogle Scholar
  3. 3.
    For an experimental review see: J.C. Wheatley, Rev. Mod. Phys. 47, 415 (1976) CrossRefADSGoogle Scholar
  4. 4.
    For a comprehensive theoretical treatment see the book by: D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990) Google Scholar
  5. 5.
    CeCu2Si2: F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, J. Schäfer, Phys. Rev. Lett. 43, 1892 (1979) CrossRefADSGoogle Scholar
  6. 6.
    UBe13: H.-R. Ott, H. Rudigier, Z. Fisk, J.L. Smith, Phys. Rev. Lett. 50, 1595 (1983) CrossRefADSGoogle Scholar
  7. 7.
    UPt3: G. Stewart, Z. Fisk, J.O. Willis, J.L. Smith, Phys. Rev. Lett. 52, 679 (1984) CrossRefADSGoogle Scholar
  8. 8.
    J.G. Bednorz, K.A. Müller, Z. Phys. B 64, 189 (1986) CrossRefADSGoogle Scholar
  9. 9.
    For a review see: C.C. Tsuei, J.R. Kirtley, Rev. Mod. Phys. 72, 969 (2000) CrossRefADSGoogle Scholar
  10. 10.
    Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J.G. Bednorz, F. Lichtenberg, Nature 372, 532 (1984) CrossRefADSGoogle Scholar
  11. 11.
    D. Einzel, J. Low Temp. Phys. 131, 1 (2003) CrossRefGoogle Scholar
  12. 12.
    D. Einzel, J.M. Parpia, Phys. Rev. B 72, 214518 (2005) CrossRefADSGoogle Scholar
  13. 13.
    For a recent review see: T.P. Devereaux, R. Hackl, Rev. Mod. Phys. 79, 175 (2007) and references therein CrossRefADSGoogle Scholar
  14. 14.
    L.J. Buchholtz, G. Zwicknagl, Phys. Rev. 23, 5788 (1981) ADSCrossRefGoogle Scholar
  15. 15.
    D. Einzel, J.M. Parpia, J. Low Temp. Phys. 109, 1 (1997) ADSGoogle Scholar
  16. 16.
    A.I. Golov, D. Einzel, G. Lawes, K. Matsumoto, J.M. Parpia, Phys. Rev. Lett. 92, 195301-1 (2004) CrossRefADSGoogle Scholar
  17. 17.
    C.J. Pethick, D. Pines, Phys. Rev. Lett. 57, 118 (1986) CrossRefADSGoogle Scholar
  18. 18.
    P. Hirschfeld, D. Vollhardt, P. Wölfle, Solid State Commun. 59, 111 (1986) CrossRefADSGoogle Scholar
  19. 19.
    For a recent review see: A.V. Balatsky, I. Vekhter, J.-X. Zhu, Rev. Mod. Phys. 78, 373 (2006) CrossRefADSGoogle Scholar
  20. 20.
    P. Hirschfeld, P. Wölfle, J.A. Sauls, D. Einzel, W.O. Puttika, Phys. Rev. 40, 6695 (1989) CrossRefADSGoogle Scholar
  21. 21.
    P.A. Lee, Phys. Rev. Lett. 71, 1887 (1993) CrossRefADSGoogle Scholar
  22. 22.
    M.J. Graf, S.-K. Yip, J.A. Sausls, D. Rainer, Phys. Rev. B 53, 15147 (1996) CrossRefADSGoogle Scholar
  23. 23.
    M.B. Walker, M.F. Smith, K.V. Samokhin, Phys. Rev. B 65, 014517-1 (2001) CrossRefADSGoogle Scholar
  24. 24.
    W.C. Wu, J.P. Carbotte, Phys. Rev. B 57, R5614 (1998); for a review see Ref. [28] CrossRefADSGoogle Scholar
  25. 25.
    H. Monien, K. Scharnberg, D. Walker, Physica B 148, 45 (1987) CrossRefGoogle Scholar
  26. 26.
    J. Moreno, P. Coleman, Phys. Rev. B 53, R2995 (1996) CrossRefADSGoogle Scholar
  27. 27.
    D. Einzel, R. Hackl, J. Raman, Spectrosc. 27, 307 (1996) ADSGoogle Scholar
  28. 28.
    T.P. Devereaux, A.P. Kampf, Int. J. Modern Phys. B 11, 2093 (1997) CrossRefADSGoogle Scholar
  29. 29.
    T.P. Devereaux, D. Einzel, Phys. Rev. B 51, 16336 (1995) CrossRefADSGoogle Scholar
  30. 30.
    P. Wölfle, D. Einzel, J. Low Temp. Phys. 23, 39 (1978) CrossRefGoogle Scholar
  31. 31.
    H. Smith, H. Hojgaard Jensen, Transport Phenomena (Clarendon, Oxford, 1989) Google Scholar
  32. 32.
    D. Einzel, D. Manske, Phys. Rev. B 70, 172507 (2004) CrossRefADSGoogle Scholar
  33. 33.
    L. Klam, Diploma thesis, unpublished (2006) Google Scholar
  34. 34.
    B. Arfi, C.J. Pethick, Phys. Rev. B 38, 2312 (1988) CrossRefADSGoogle Scholar
  35. 35.
    R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, Adv. Comput. Math. 5 4, 329 (1996) and references therein CrossRefMathSciNetGoogle Scholar
  36. 36.
    J.P. Rodriguez, Phys. Rev. Lett. 55, 250 (1985) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Walther-Meissner-Institut für TieftemperaturforschungGarchingGermany

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