Microscopic quantum interference in the theory of superconductivity

JUL 01, 1973

“…an outline of some of the main features of our 1957 theory, an indication of directions taken since and a discussion of quantum–interference effects due to the singlet–spin pairing in superconductors.”

DOI: 10.1063/1.3128139

Leon N. Cooper

It is an honor and a pleasure to speak to you today about the theory of superconductivity. In a short lecture one can no more than touch on the long history of experimental and theoretical work on this subject before 1957. Nor can one hope to give an adequate account of how our understanding of superconductivity has evolved since that time. The theory we presented in 1957, applied to uniform materials in the weak‐coupling limit so defining an ideal superconductor, has been extended in almost every imaginable direction. To these developments so many authors have contributed that we can make no pretense of doing them justice. I will confine myself here to an outline of some of the main features of our 1957 theory, an indication of directions taken since and a discussion of quantum interference effects due to the single‐spin pairing in superconductors which might be considered the microscopic analogue of the effects discussed by Professor Schrieffer.

This article is only available in PDF format

References

1. J. Bardeen, L. N. Cooper, J. R. Schrieifer, Phys. Rev. 108, 1175 (1957).https://doi.org/PHRVAO
2. An account of the situation as of 1969 may be found in the two volumes: Superconductivity, R. D. Parks, ed. Marcel Dekker, New York (1969).
3. A. Sommerfeld, Z. Physik 47, 1 (1928)https://doi.org/ZEPYAA
F. Bloch, Z. Physik 52, 555 (1928).https://doi.org/ZEPYAA
4. D. D. Osheroff, W. J. Gully, R. C. Richardson, D. M. Lee, Phys. Rev. Lett. 29, 920 (1972); https://doi.org/PRLTAO
A. J. Leggett, Phys. Rev. Lett. 29, 1227 (1972).https://doi.org/PRLTAO
5. N. N. Bogoliubov, Nuovo Cimento 7, 794 (1958); https://doi.org/NUCIAD
Usp. Fiz. Nauk 67, 549 (1959); https://doi.org/UFNAAG
J. G. Valatin, Nuovo Cimento 7, 843 (1958).https://doi.org/NUCIAD
6. J. Bardeen, G. Rickayzen, Phys. Rev. 118, 936 (1960); https://doi.org/PHRVAO
D. C. Mattis, E. Lieb, J. Math. Phys. 2, 602 (1961); https://doi.org/JMAPAQ
N. N. Bogoliubov, D. N. Zubarev, Yu. A. Tserkovnikov, Zh. Eksperim. i Teor. Fiz. 39, 120 (1960),
translated in N. N. Bogoliubov, D. N. Zubarev, Yu. A. Tserkovnikov, Sov. Phys. JETP 12, 88 (1961).https://doi.org/SPHJAR
7. See, for example, R. E. GloverIII, M. Tinkham, Phys. Rev. 108, 243 (1957); https://doi.org/PHRVAO
M. A. Biondi, M. P. Garfunkel, Phys. Rev. 116, 853 (1959).https://doi.org/PHRVAO
8. The importance of the coupling of timereversed states in constructing electron pairs was emphasized by P. W. Anderson;
see, for example, P. W. Anderson, J. Phys. Chem. Solids 11, 26 (1959).https://doi.org/JPCSAW
9. (a) L. C. Hebel, C. P. Slichter, Phys. Rev. 113, 1504 (1959). https://doi.org/PHRVAO
(b) A. G. Redfield, A. G. Anderson, Phys. Rev. 116, 583 (1959).https://doi.org/PHRVAO
10. (a) H. E. Bommel, Phys. Rev. 96, 220 (1954). https://doi.org/PHRVAO
(b) R. W. Morse, H. V. Bohm, Phys. Rev. 108, 1094 (1957).https://doi.org/PHRVAO
11. M. Fibich, Phys. Rev. Lett. 14, 561 (1965).https://doi.org/PRLTAO
12. See, for example, T. Tsuneto, Phys. Rev. 121, 402 (1961).https://doi.org/PHRVAO
13. L. P. Gor’kov, Zh. Eksperim. i Teor. Fiz. 34, 735 (1958),
translated in L. P. Gor’kov, Sov. Phys. JETP 7, 505 (1958); https://doi.org/SPHJAR
P. C. Martin, J. Schwinger, Phys. Rev. 115, 1342 (1959); https://doi.org/PHRVAO
L. P. Kadanoff, P. C. Martin, Phys. Rev. 124, 670 (1961).https://doi.org/PHRVAO
14. A. A. Abrikosov, L. P. Gor’kov, Zh. Eksperim. i Teor. Fiz. 39, 1781 (1960),
translated in A. A. Abrikosov, L. P. Gor’kov, Sov. Phys. JETP 12, 1243 (1961); https://doi.org/SPHJAR
P. G. de Gennes, Superconductivity of Metals and Alloys, Benjamin, New York (1966).
15. See for example, V. Ambegaokar, L. P. Kadanoff, Nuovo Cimento 22, 914 (1961).https://doi.org/NUCIAD
16. See for example, C. Caroli, J. Matricon, Physik Kondensierten Materie 3, 380 (1965); https://doi.org/PKOMA3
K. Maki, Phys. Rev. 141, 331 (1966), https://doi.org/PHRVAO
and 156, 437 (1967); https://doi.org/PHRVAO , Phys. Rev.
Groupe de Supraconductivité d’Orsay, Physik Kondersierten Materie 5, 141 (1966);
D. Eppel, W. Pesch, L. Tewordt, Z. Physik 197, 46 (1966); https://doi.org/ZEPYAA
F. P. McLean, A. Houghton, Annals of Physics 48, 43 (1968).https://doi.org/ANPYA2
17. A. Bohr, B. R. Mottelson, D. Pines, Phys. Rev. 110, 936 (1958); https://doi.org/PHRVAO
A. B. Migdal, Nuclear Phys. 13, 655 (1959). https://doi.org/NUPHA7
18. V. L. Ginzburg, D. A. Kirzhnits, Zh. Eksperim, i Theor. Fiz. 47, 2006 (1964),
translated in Sov. Phys. JETP 20, 1346 (1965); https://doi.org/SPHJAR
D. Pines, G. Baym, C. Pethick, Nature 224, 673 (1969).https://doi.org/NATUAS
19. Many authors have explored the possibility of a superconducting‐like transition in He3. Among the most recent contributions see reference 4.
20. See, for example, Y. Nambu, G. Jona‐Lasinio, Phys. Rev. 122, 345 (1961).https://doi.org/PHRVAO
21. J. Goldstone, Nuovo Cimento 19, 154 (1961); https://doi.org/NUCIAD
S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).https://doi.org/PRLTAO
22. Henri Poincaré, La Science et l’Hypothèse, Flammarion, Paris, (1902), page 168. “The scientist must order; science is made with facts as a house with stones; but an accumulation of facts is no more a science than a heap of stones is a house.”

More about the authors

Leon N. Cooper, Brown University, Providence, R.I..