Journal of Low Temperature Physics

, Volume 114, Issue 1–2, pp 257–273 | Cite as

Thermal Conductivity of the Accidental Degeneracy and Enlarged Symmetry Group Models for Superconducting UPt3

  • M. J. Graf
  • S.-K. Yip
  • J. A. Sauls
Article

Abstract

We present theoretical calculations of the thermal conductivity for the “accidental degeneracy” and “enlarged symmetry group” models that have been proposed to explain the phase diagram of UPt3. The order parameters for these models possess point nodes or cross nodes, reflecting the broken symmetries of the ground state. These broken symmetries lead to robust predictions for the ratio of the low-temperature thermal conductivity for heat flow along the ĉ axis and in the basal plane. The anisotropy of the heat current response at low temperatures is determined by the phase space for scattering by impurities. The measured anisotropy ratio, κc/κb, provides a strong constraint on theoretical models for the ground state order parameter. The accidental degeneracy and enlarged symmetry group models based on no spin-orbit coupling do not account for the thermal conductivity of UPt3. The models for the order parameter that fit the experimental data for the ĉ and \({\hat c}\) directions of the heat current are the 2D E1gand E2umodels, for which the order parameters possess line nodes in the ab-plane and point nodes along the ĉ axis, and the A1gE1gmodel of Zhitomirsky and Ueda. This model spontaneously breaks rotational symmetry in the ab-plane below Tc2and predicts a large anisotropy for the ab-plane heat current.

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REFERENCES

  1. 1.
    V. Müller, Ch. Roth, D. Maurer, E. W. Scheidt, and K. Lüders, Phys. Rev. Lett. 58, 1224 (1987).Google Scholar
  2. 2.
    Y. Qian, M. Xu, A. Schenstrom, H.-P. Baum, J. B. Ketterson, D. Hinks, M. Levy, and B. K. Sarma, Solid State Commun. 63, 599 (1987).Google Scholar
  3. 3.
    G. Bruls, D. Weber, B. Wolf, P. Thalameier, B. Lüthi, A. de Visser, and A. Menovsky, Phys. Rev. Lett. 65, 2294 (1990).Google Scholar
  4. 4.
    S. Adenwalla, S. W. Lin, Z. Zhao, Q. Z. Ran, J. B. Ketterson, J. A. Sauls, L. Taillefer, D. G. Hinks, M. Levy, and B. K. Sarma, Phys. Rev. Lett. 65, 2298 (1990).Google Scholar
  5. 5.
    S. Hayden, L. Taillefer, C. Vettier, and J. Flouquet, Phys. Rev. B 46, 8675 (1992).Google Scholar
  6. 6.
    P. A. Midgley, S. M. Hayden, L. Taillefer, B. Bogenberger, and H. von Löhneysen, Phys. Rev. Lett. 70, 678 (1993).Google Scholar
  7. 7.
    V. Mineev, Sov. Phys. JETP Lett. 57, 683 (1993).Google Scholar
  8. 8.
    B. Ellman, A. Zaluska, and L. Taillefer, Physica B 205, 346 (1995); B. Ellman, LANL E-print http://xxx.lanl.gov/abs/cond-mat/9704125.Google Scholar
  9. 9.
    I. Luk'yanchuk, J. Phys. 11, 1155 (1991).Google Scholar
  10. 10.
    D. Chen and A. Garg, Phys. Rev. Lett. 70, 1689 (1993).Google Scholar
  11. 11.
    K. Machida and M. Ozaki, Phys. Rev. Lett. 66, 3293 (1991).Google Scholar
  12. 12.
    J. Sauls, Adv. Phys. 43, 113 (1994).Google Scholar
  13. 13.
    K. Park and R. Joynt, Phys. Rev. B 53, 12346 (1996).Google Scholar
  14. 14.
    B. Shivaram, T. Rosenbaum, and D. Hinks, Phys. Rev. Lett. 57, 1259 (1986).Google Scholar
  15. 15.
    N. Keller, J. L. Tholence, A. Huxley, and J. Flouquet, Phys. Rev. Lett. 73, 2364 (1994).Google Scholar
  16. 16.
    C. Choi and J. Sauls, Phys. Rev. Lett. 66, 484 (1991).Google Scholar
  17. 17.
    H. Tou, Y. Kitaoka, K. Ishida, K. Asayama, and N. Kimura, Phys. Rev. Lett. 80, 3129 (1998).Google Scholar
  18. 18.
    T. Ohmi and K. Machida, Phys. Rev. Lett. 71, 625 (1993).Google Scholar
  19. 19.
    K. Machida, T. Ohmi, and M. Ozaki, J. Phys. Soc. Jpn. 62, 3216 (1993).Google Scholar
  20. 20.
    K. Machida and T. Ohmi, J. Phys. soc. Jpn. 65, 3456 (1996).Google Scholar
  21. 21.
    M. Zhitomirskii and I. Luk'yanchuk, Sov. Phys. JETP Lett. 58, 131 (1993).Google Scholar
  22. 22.
    M. Zhitomirskii and K. Ueda, Phys. Rev. B 53, 6591 (1996).Google Scholar
  23. 23.
    R. Heffner and M. Norman, Comm. Cond. Matt. Phys. 17, 361, (1996).Google Scholar
  24. 24.
    J. A. Sauls and D. Rainer, Czech. J. Phys. 47, 1065 (1996).Google Scholar
  25. 25.
    P. J. Hirschfeld, D. Vollhardt, and P. Wölfle, Sol. State Comm. 59, 111 (1986).Google Scholar
  26. 26.
    C. Choi and P. Muzikar, Phys. Rev. B 36, 54 (1987).Google Scholar
  27. 27.
    M. J. Graf, S.-K. Yip, J. A. Sauls, and D. Rainer, Phys. Rev. B 53, 15147 (1996).Google Scholar
  28. 28.
    M. J. Graf, S.-K. Yip, and J. A. Sauls, J. Low Temp. Phys. 102, 367 (1996); 106, 727 (1997).Google Scholar
  29. 29.
    B. Lussier, B. Ellman, and L. Taillefer, Phys. Rev. B 53, 5145 (1996).Google Scholar
  30. 30.
    H. Suderow, J. P. Brison, A. Huxley, and J. Flouquet, J. Low Temp. Phys. 108, 11 (1997).Google Scholar
  31. 31.
    M. Norman and P. Hirschfeld, Phys. Rev. B 53 5706 (1996).Google Scholar
  32. 32.
    L. J. Buchholtz and G. Zwicknagl, Phys. Rev. B 23, 5788 (1981).Google Scholar
  33. 33.
    G. Preosti, H. Kim, and P. Muzikar, Phys. Rev. B 50, 1259 (1994).Google Scholar
  34. 34.
    A. Balatsky, M. L. Salkola, and A. Rosengreen, Phys. Rev. B 51, 15547 (1995).Google Scholar
  35. 35.
    L. Gor'kov and P. A. Kalugin, Sov. Phys. JETP Lett. 41, 254 (1985).Google Scholar
  36. 36.
    C. Choi and P. Muzikar, Phys. Rev. B 37, 5947 (1988).Google Scholar
  37. 37.
    P. A. Lee, Phys. Rev. Lett. 71, 1887 (1993).Google Scholar
  38. 38.
    M. J. Graf, M. Palumbo, D. Rainer, and J. A. Sauls, Phys. Rev. B 52, 10588 (1995).Google Scholar
  39. 39.
    Y. Sun and K. Maki, Euro. Phys. Lett. 32, 355 (1995).Google Scholar
  40. 40.
    B. Shivaram, Y. Jeong, T. Rosenbaum, and D. Hinks, Phys. Rev. Lett. 56, 1078 (1986).Google Scholar
  41. 41.
    C. Broholm, G. Aeppli, R. Kleiman, D. R. Harshman, D. J. Bishop, E. Bucher, D. Williams, E. Ansaldo, and R. Heffner, Phys. Rev. Lett. 65, 1078 (1990).Google Scholar
  42. 42.
    K. Miyake, S. Schmitt-Rink, and C. Varma, Phys. Rev. B 34, 6554 (1986).Google Scholar
  43. 43.
    S. Schmitt-Rink, K. Miyake, and C. Varma, Phys. Rev. Lett. 57, 2575 (1986).Google Scholar
  44. 44.
    H. Monien, K. Scharnberg, L. Tewordt, and N. Schopohl, J. Low Temp. Phys. 65, 13 (1986).Google Scholar
  45. 45.
    C. J. Pethick and D. Pines, Phys. Rev. Lett. 57, 118 (1986).Google Scholar
  46. 46.
    S. Yip and A. Garg, Phys. Rev. B 48, 3304 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • M. J. Graf
    • 1
    • 2
  • S.-K. Yip
    • 1
  • J. A. Sauls
    • 1
  1. 1.Department of Physics & AstronomyNorthwestern UniversityEvanstonUSA
  2. 2.Center for Materials ScienceLos Alamos National LaboratoryLos AlamosUSA

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