Skip to main content
Log in

Stability of superconducting states out of thermal equilibrium

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

Quasiparticles of superconductors can be manipulated either by irradiation or tunnel injection such that substantial changes of the gap (order parameter) occur which are most pronounced close to the transition temperature. These phenomena are investigated by a theory which is based on the combined system of the Boltzmann equation and the BCS gap equation. Several stationary, spatially homogeneous states are found in some range of temperatures. A linear stability analysis reveals two types of behavior, depending, essentially, on whether quasiparticle diffusion increases or decreases the stability. In a representative situation of the first type, two states turn out to be locally stable. An investigation of a nonlinear equation of motion for the order parameter leads to the conclusion that a first-order phase transition between these two states occurs at a given temperature. In a situation of the second type, one finds that fluctuations of a definite wave vector destroy the spatially homogeneous state and lead to a stable state of layered structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. N. Langenberg, in Low Temperature Physics—LT14, M. Krusius and M. Vuorio, eds. (North-Holland, Amsterdam, 1975).

    Google Scholar 

  2. Albert Schmid, in Proc. LT 15, J. Phys. (Paris) 39, C-6 (1978).

    Google Scholar 

  3. H. Haken, Rev. Mod. Phys. 47, 67 (1975).

    Article  ADS  Google Scholar 

  4. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  5. J. Bardeen, G. Rickayzen, and L. Tewordt, Phys. Rev. 113, 982 (1958).

    Article  ADS  Google Scholar 

  6. A. G. Aronov and V. L. Gurevich, Fiz. Tverd. Tela 16, 2656 (1974) [Sov. Phys.—Solid State 16, 1722 (1975)].

    Google Scholar 

  7. V. F. Elesin, Zh. Eksp. Teor. Fiz. 71, 1490 (1976) [Sov. Phys.—JETP 44, 780 (1976)].

    Google Scholar 

  8. G. M. Eliashberg, Zh. Eksp. Teor. Fiz. 61, 1254 (1971) [Sov. Phys.—JETP 34, 668 (1972)].

    Google Scholar 

  9. Albert Schmid and Gerd Schön, J. Low Temp. Phys. 20, 207 (1975).

    Article  ADS  Google Scholar 

  10. A. I. Larkin and Yu. N. Ovchinnikov, Zh. Eksp. Teor. Fiz. 73, 299 (1977) [Sov. Phys.—JETP 46, 155 (1978)].

    ADS  Google Scholar 

  11. Albert Schmid, Phys. Rev. Lett. 38, 922 (1977).

    Article  ADS  Google Scholar 

  12. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963), Vol. 1.

    MATH  Google Scholar 

  13. H. A. Kramers, Physica VII, 284 (1940).

    Article  ADS  MathSciNet  Google Scholar 

  14. R. Landauer and J. A. Swanson, Phys. Rev. 121, 1668 (1961).

    Article  ADS  Google Scholar 

  15. J. S. Langer, Phys. Rev. Lett. 21, 973 (1968).

    Article  ADS  Google Scholar 

  16. D. E. McCumber and B. I. Halperin, Phys. Rev. B 1, 1054 (1970).

    Article  ADS  Google Scholar 

  17. J. Blot, Y. Pellan, and J. Rosenblatt, J. Low Temp. Phys. 30, 669 (1978).

    Article  ADS  Google Scholar 

  18. R. Landauer, Phys. Rev. A 15, 2117 (1977).

    Article  ADS  Google Scholar 

  19. R. Graham and H. Haken, Z. Phys. 243, 289 (1971).

    Article  ADS  Google Scholar 

  20. G. M. Eliashberg, Pis'ma Zh. Eksp. Teor. Fiz. 11, 186 (1970) [JETPLett. 11, 114 (1970)]; see also B. I. Ivlev, S. G. Lisitsyn, and G. M. Eliashberg, J. Low Temp. Phys. 10, 449 (1973).

    Google Scholar 

  21. C. C. Chi and John Clarke, preprint.

  22. R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys. Rev. Lett. 39, 229 (1977).

    Article  ADS  Google Scholar 

  23. Gerd Schön and André-M. Tremblay, Phys. Rev. Lett. 42, 1086 (1979).

    Article  ADS  Google Scholar 

  24. J. J. Chang and D. J. Scalapino, Phys. Rev. B 15, 2651 (1977).

    Article  ADS  Google Scholar 

  25. C. S. Owen and D. J. Scalapino, Phys. Rev. Lett. 28, 1559 (1972).

    Article  ADS  Google Scholar 

  26. J. J. Chang and D. J. Scalapino, Phys. Rev. B 10, 4047, (1974).

    Article  ADS  Google Scholar 

  27. D. J. Scalapino and B. A. Huberman, Phys. Rev. Lett. 39, 1365 (1977).

    Article  ADS  Google Scholar 

  28. A. Rothwarf and B. N. Taylor, Phys. Rev. Lett. 19, 27 (1967).

    Article  ADS  Google Scholar 

  29. K. Hida, J. Low Temp. Phys. 32, 881 (1978).

    Article  ADS  Google Scholar 

  30. L. N. Smith, J. Low Temp. Phys. 28, 519 (1977).

    Article  ADS  Google Scholar 

  31. B. I. Ivlev, Zh. Eksp. Teor. Fiz. 72, 1197 (1977) [Sov. Phys.—JETP 45, 626 (1977)].

    Google Scholar 

  32. V. F. Elesin, Zh. Eksp. Teor. Fiz. 73, 355 (1977) [Sov. Phys.—JETP 46, 185 (1977)].

    ADS  Google Scholar 

  33. K. Hida, Phys. Lett. 68A, 71 (1978).

    Article  ADS  Google Scholar 

  34. M. Weite, Z. Phys. B 29, 107 (1978).

    Article  ADS  Google Scholar 

  35. T. J. Tredwell and E. H. Jakobsen, Phys. Rev. B 13, 2931 (1976).

    Article  ADS  Google Scholar 

  36. T. M. Klapwijk, J. N. van den Bergh, and J. E. Mooij, J. Low Temp. Phys. 26, 385 (1977).

    Article  ADS  Google Scholar 

  37. Yu. I. Latyshev and F. Ya. Nad', Pis'ma Zh. Eksp. Teor. Fiz. 26, 488 (1977).

    Google Scholar 

  38. T. Kommers and J. Clarke, Phys. Rev. Lett. 38, 1091 (1977).

    Article  ADS  Google Scholar 

  39. J. A. Pals, Phys. Lett. 63A, 141 (1977).

    Article  ADS  Google Scholar 

  40. K. E. Gray and H. W. Willemisen, J. Low Temp. Phys. 31, 911 (1978).

    Article  ADS  Google Scholar 

  41. J. Fuchs, P. W. Epperlein, M. Welte, and W. Eisenmenger, Phys. Rev. Lett. 38, 919 (1977).

    Article  ADS  Google Scholar 

  42. G. A. Sai-Halasz, C. C. Chi, A. Denenstein, and D. N. Langenberg, Phys. Rev. Lett. 33, 215 (1974).

    Article  ADS  Google Scholar 

  43. A. A. Golovashkin, K. V. Mitsen, and G. P. Motulevich, Zh. Eksp. Teor. Fiz. 68, 1408 (1975) [Sov. Phys.—JETP 41, 701 (1976)].

    ADS  Google Scholar 

  44. I. Iguchi, J. Low Temp. Phys. 33, 439 (1978).

    Article  ADS  Google Scholar 

  45. W. J. Skocpol, M. R. Beasley, and M. Tinkham, J. Low Temp. Phys. 16, 145 (1974).

    Article  ADS  Google Scholar 

  46. L. Kramer and A. Baratoff, Phys. Rev. Lett. 38, 518 (1977); L. Kramer and R. J. Watts-Tobin, Phys. Rev. Lett. 40, 1041 (1978).

    Article  ADS  Google Scholar 

  47. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer Verlag, Berlin, 1971).

    Book  MATH  Google Scholar 

  48. W. Dupont, Diplomarbeit, Karlsruhe (1977).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eckern, U., Schmid, A., Schmutz, M. et al. Stability of superconducting states out of thermal equilibrium. J Low Temp Phys 36, 643–687 (1979). https://doi.org/10.1007/BF00116992

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00116992

Keywords

Navigation