Journal of Low Temperature Physics

, Volume 86, Issue 3–4, pp 257–290 | Cite as

Circular dichroism and birefringence in unconventional superconductors

  • S. K. Yip
  • J. A. Sauls
Article

Abstract

We present a theoretical analysis of circular dichroism and birefringe in unconventional BCS superconductors with appropriate broken symmetries. We show that for the effect to exist, that in addition to broken time-reversal and two-dimensional parity symmetries, it is necessary to take into account the weak particle-hole asymmetry of the low-energy excitations of the metallic state. Circular dichroism and birefringence are shown to arise from the order parameter collective mode response of the superconductor; in the clean limit the contribution to the current response from the single-particle excitations does not give rise to circular dichroism or birefringence, even with particle-hole asymmetry. The magnitude of the circular dichroism is found to be small for the classes of superconductors which are thought to be likely candidates to exhibit the requisite broken symmetries, namely the heavy fermions and oxide superconductors. The order of magnitude of the elliptical polarization of a linearly polarized incident wave is Vf/c(ζ/λL) (Δ/Ef) ln(Ef/Δ), which is roughly 10−7−10−8 rad at frequencies of order the gap, and decreases at least as fast as (2Δ/ω)2 at higher frequencies.

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References

  1. 1.
    J. Bardeen, L. N. Cooper, and R. Schrieffer,Phys. Rev. 108, 1175 (1957).Google Scholar
  2. 2.
    P. W. Anderson,Basic Notions of Condensed Matter (Benjamin Cummings, Menlo Park, 1984).Google Scholar
  3. 3.
    L. P. Gorkov,Sov. Sci. Rev. A9, 1 (1987).Google Scholar
  4. 4.
    D. Rainer,Phys. Scr. T23, 106 (1988).Google Scholar
  5. 5.
    M. Sigrist and K. Ueda,Rev. Mod. Phys. 63, 239 (1991).Google Scholar
  6. 6.
    J. Annett,Adv. Phys. 39, 83 (1990).Google Scholar
  7. 7.
    A. J. Leggett,Rev. Mod. Phys. 47, 331 (1975).Google Scholar
  8. 8.
    L. P. Gorkov,JETP Lett. 40, 1155 (1984).Google Scholar
  9. 9.
    C. H. Choi and P. Muzikar,Phys. Rev. B37, 5947 (1988).Google Scholar
  10. 10.
    P. Hirschfeld,Phys. Rev. B37, 9331 (1988).Google Scholar
  11. 11.
    B. Arfi, H. Bahlouli, and C. J. Pethick,Phys. Rev. B39, 8959 (1989).Google Scholar
  12. 12.
    R. Joynt,Sup. Sci. Tech. 1, 210 (1988).Google Scholar
  13. 13.
    D. Hess, T. Tokuyasu, and J. A. Sauls,J. Phys. Cond. Matt. 1, 8135 (1989).Google Scholar
  14. 14.
    K. Machida and M. Ozaki,J. Phys. Soc. Jpn. 58, 2244 (1989).Google Scholar
  15. 15.
    E. Blount, C. Varma, and G. Appeli,Phys. Rev. Lett. 64, 3074 (1990).Google Scholar
  16. 16.
    C. H. Choi and P. Muzikar,Phys. Rev. B39, 9664 (1989).Google Scholar
  17. 17.
    T. Tokuyasu, D. Hess, and J. A. Sauls,Phys. Rev. B41, 8891 (1990).Google Scholar
  18. 18.
    V. Kalmeyer and R. B. Laughlin,Phys. Rev. Lett. 59, 2095 (1987).Google Scholar
  19. 19.
    B. I. Halperin, J. March-Russell, and F. Wilczek,Phys. Rev. B40, 8726 (1989).Google Scholar
  20. 20.
    X. G. Wen and A. Zee,Phys. Rev. Lett. 62, 2873 (1988).Google Scholar
  21. 21.
    K. B. Lyons, J. Kwo, J. F. Dillon Jr., G. P. Espinosa, M. McGlashan-Powell, A. P. Ramirez, and L. F. Schneemeyer,Phys. Rev. Lett. 64, 2949 (1990).Google Scholar
  22. 22.
    K. B. Lyons, J. F. Dillon Jr., E. S. Hellman, E. H. Hartford, and M. McGlashan-Powell,Phys. Rev. B43, 11408 (1991).Google Scholar
  23. 23.
    S. Spielman, K. Fesler, C. B. Eom, T. H. Geballe, M. M. Fejer, and A. Kapitulnik,Phys. Rev. Lett 65, 123 (1990).Google Scholar
  24. 24.
    H. J. Weber, D. Weitbrecht, D. Brach, A. L. Shelankov, H. Keiter, W. Weber, Th. Wolf, J. Geerk, G. Linker, G. Roth, P. C. Splittgerber-Hünnekes, and G. Güntherodt,Sol. State Comm. 76, 511 (1990).Google Scholar
  25. 25.
    P. W. Anderson and P. Morel,Phys. Rev. 123, 1911 (1961).Google Scholar
  26. 26.
    R. McKenzie and J. A. Sauls,Helium Three (Elsevier, Amsterdam, 1991), p. 255.Google Scholar
  27. 27.
    W. P. Halperin and E. Varoquauz,Helium Three (Elsevier, Amsterdam, 1991), p. 353.Google Scholar
  28. 28.
    J. W. Serene,Quantum Fluids and Solids (American Institute of Physics, New York, 1983), p. 305.Google Scholar
  29. 29.
    R. S. Fishman and J. A. Sauls,Phys. Rev. 31, 251 (1985).Google Scholar
  30. 30.
    G. Eilenberger,Z. Phys. 214, 195 (1968).Google Scholar
  31. 31.
    G. M. Eliashberg,Sov. Phys.-JETP 34, 668 (1972).Google Scholar
  32. 32.
    A. I. Larkin and Yu. N. Ovchinnikov,Sov. Phys.-JETP 28, 1200 (1969).Google Scholar
  33. 33.
    J. W. Serene and D. Rainer,Phys. Rep. 101, 221 (1983).Google Scholar
  34. 34.
    P. Wölfle,Prog. in Low Temperature Physics VIIA (North-Holland, Amsterdam, 1983).Google Scholar
  35. 35.
    P. Wölfle,Physica 90B, 96 (1977).Google Scholar
  36. 36.
    P. J. Hirschfeld, P. Wölfle, D. Einzel, J. Sauls, and W. Puttika,Phys. Rev. B40, 6695 (1989).Google Scholar
  37. 37.
    P. Wölfle and V. E. Koch,J. Low. Temp. Phys. 30, 61 (1978).Google Scholar
  38. 38.
    H. Monien, K. Scharnberg, L. Tewordt, and N. Schopohl,J. Low. Temp. Phys. 65, 13 (1986).Google Scholar
  39. 39.
    Q. P. Li and R. Joynt,Phys. Rev. B44, 4720 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • S. K. Yip
    • 1
  • J. A. Sauls
    • 1
  1. 1.Science and Technology Center for Superconductivity and Department of Physics & AstronomyNorthwestern UniversityEvanston

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