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Proximity effect in superconductors: Calculation of the transition temperature

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Abstract

The problem of the calculation of the transition temperature in the proximity effect is considered. From the variational principle of Silvert and Cooper we derive a simpler variational principle which is useful in obtaining a rapid numerical estimate of the transition temperature as well as the qualitative features of the solution. Approximate and exact solutions for the transition temperature and the order parameter are obtained in the clean limit, the geometry investigated being that of a superconducting sphere embedded in an infinite normal matrix. The results for the transition temperature do not display the unphysical behavior found in previous work in the clean limit and suggest that there is a critical radius for the sphere below which the sample is normal at all temperatures. The results for the order parameter show that the nonanalytic behavior discovered by Silvert and Cooper is a relatively small effect in the case investigated.

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References

  1. A. L. Fetter and J. D. Walecka,Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).

    Google Scholar 

  2. P. G. de Gennes and E. Guyon,Phys. Letters 3, 168 (1963).

    Google Scholar 

  3. N. R. Werthamer,Phys. Rev. 132, 2442 (1963).

    Google Scholar 

  4. P. G. de Gennes,Rev. Mod. Phys. 36, 225 (1964).

    Google Scholar 

  5. A. E. Jacobs,Phys. Rev. 162, 375 (1967).

    Google Scholar 

  6. L. N. Cooper,Phys. Rev. Letters 6, 689 (1961).

    Google Scholar 

  7. W. Silvert,Zh. Eksperim. i Teor. Fiz. 53, 1693 (1967) [English transl.,Soviet Phys.—JETP 26, 971 (1968)].

    Google Scholar 

  8. W. Moormann,Z. Physik 197, 136 (1966).

    Google Scholar 

  9. W. Silvert and L. N. Cooper,Phys. Rev. 141, 336 (1966).

    Google Scholar 

  10. W. Silvert and A. Singh,Phys. Rev. Letters 28, 222 (1972).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Toronto, Toronto, Ontario, Canada

    K. M. Hong & A. E. Jacobs

Authors
  1. K. M. Hong
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  2. A. E. Jacobs
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Additional information

Supported in part by the National Research Council of Canada and in part by Scarborough College, University of Toronto.

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Hong, K.M., Jacobs, A.E. Proximity effect in superconductors: Calculation of the transition temperature. J Low Temp Phys 12, 519–527 (1973). https://doi.org/10.1007/BF00654954

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  • DOI: https://doi.org/10.1007/BF00654954

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