The Gor'kov theory of the proximity effect has been solved to a high degree of accuracy by a numerical variational method for a system of two metallic films of finite thickness. The results are analyzed in the context of exact sum rules for the Gor'kov theory and compared with those obtained from various approximate theories, including diffusion theories. It is found that for thin films the order parameter varies considerably more rapidly than is predicted by local theories (e.g., Ginzburg-Landau) and that the different diffusion theories are quite unreliable.
Similar content being viewed by others
References
J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
W. Silvert and L. N. Cooper, Phys. Rev. 141, 336 (1966).
L. P. Gor'kov, Zh. Eksp. Teor. Fiz. 34, 735 (1958) [English transl., Soviet Phys.—JETP 7, 505 (1958)].
W. L. McMillan, Phys. Rev. 175, 537 (1968).
P. G. de Gennes, Rev. Mod. Phys. 36, 225 (1964).
N. R. Werthamer, Phys. Rev. 132, 2440 (1963).
W. Silvert, Zh. Eksp. Teor. Fiz. 53, 1693 (1967) [English transl., Soviet Phys.—JETP 26, 971 (1968)].
A. A. Abrikosov and L. P. Gor'kov, Zh. Eksp. Teor. Fiz. 35, 1558 (1958) [English transl., Soviet Phys.—JETP 8, 1090 (1959)].
W. Silvert, Physics 2, 153 (1966).
T. Matsubara, Prog. Theor. Phys. (Kyoto) 14, 351 (1955).
A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963), pp. 325–334.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1964).
W. Silvert and A. Singh, Phys. Rev. Lett. 28, 222 (1972).
W. Silvert, Solid State Comm. 14, 635 (1974).
H. J. Fink and A. G. Presson, Phys. Rev. B 1, 221 (1970).
H. J. Fink and P. Martinoli, J. Low Temp. Phys. 4, 305 (1971).
P. G. de Gennes and E. Guyon, Phys. Lett. 3, 168 (1963).
W. Moormann, Z. Physik 197, 136 (1966).
W. L. McMillan, Phys. Rev. 167, 331 (1968).
W. Silvert, Ph.D. Thesis, Brown University, 1965, p. 14.
G. M. Eliashberg, Zh. Eksp. Teor. Fiz. 38, 966 (1960); 39, 143 (1960) [English transl., Soviet Phys.—JETP 11, 696 (1960); 12, 1000 (1961)].
W. Silvert, in Proc. 10th Int. Conf. Low Temp. Phys. (Moscow, 1967), Vol. 2a, pp. 226–227.
A. B. Pippard, Rep. Prog. Phys. 23, 176 (1960).
J. J. Hauser, H. C. Theuerer, and N. R. Werthamer, Phys. Rev. 136, A637 (1964).
E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, 1970), pp. 48–51.
K. M. Hong and A. E. Jacobs, J. Low Temp. Phys. 12, 519 (1973).
R. H.-T. Yeh, Ph.D. Thesis, University of Illinois, 1967.
R. Singh, M.Sc. Thesis, Dalhousie University, 1974, pp. 27–39.
L. N. Cooper, Phys. Rev. Lett. 6, 689 (1961).
A. E. Jacobs, Phys. Rev. 162, 375 (1967).
R. H.-T. Yeh, Ann. Phys. (N.Y.) 46, 546 (1968).
V. Kourganoff, Basic Methods in Transfer Problems (Dover, 1963), pp. 174ff.
G. I. Bell and S. Glasstone, Nuclear Reactor Theory (van Nostrand Reinhold, 1970), pp. 95–97.
Author information
Authors and Affiliations
Additional information
Supported by the National Research Council of Canada.
Rights and permissions
About this article
Cite this article
Silvert, W. Theory of the superconducting proximity effect. J Low Temp Phys 20, 439–477 (1975). https://doi.org/10.1007/BF00120864
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00120864