Intrinsic Fluctuations in Superconducting Rings Containing One-Dimensional Weak Links

D. E. McCumber

doi:10.1103/PhysRev.181.716

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Intrinsic Fluctuations in Superconducting Rings Containing One-Dimensional Weak Links

D. E. McCumber

Bell Telephone Laboratories, Murray Hill, New Jersey 07974

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Phys. Rev. 181, 716 – Published 10 May, 1969

DOI: https://doi.org/10.1103/PhysRev.181.716

Abstract

The Langer-Ambegaokar statistical theory of dissipative fluctuations in narrow superconducting channels is extended to describe the quantum transitions of a closed superconducting ring containing a long one-dimensional weak-link section. The external magnetic flux $Φ_{e}$ linking the loop is the independent thermo-dynamic variable. Based upon the Ginzburg-Landau free energy, the theory is expected to accurately describe single-quantum transitions for $T$ near but slightly below $T_{c}$ . Data reported by Lukens and Good-kind for thin-film Sn rings are reasonably consistent with the theory, but more definitive experimental tests are required.

References (31)

J. S. Langer and V. Ambegaokar, Phys. Rev. 164, 498 (1967)
W. W. Webb and R. J. Warburton, Phys. Rev. Letters 20, 461 (1968)
J. Franks, Acta Met. 6, 103 (1958) C. Herring and J. K. Galt, Phys. Rev. 85, 1060 (1952)
D. E. McCumber, Phys. Rev. 172, 427 (1968)
R. D. Parks, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 141
R. D. Parks and R. P. Groff, Phys. Rev. Letters 18, 342 (1967)
T. K. Hunt and J. E. Mercereau, Phys. Rev. Letters 18, 551 (1967)
R. P. Groff, S¨. Marčelja, W. E. Masker, and R. D. Parks, Phys. Rev. Letters 19, 1328 (1967)
J. E. Zimmerman and A. H. Silver, Phys. Rev. Letters 19, 14 (1967) A. H. Silver and J. E. Zimmerman, Phys. Rev. 157, 317 (1967)
J. E. Lukens and J. M. Goodkind, Phys. Rev. Letters 20, 1363 (1968)
J. S. Langer, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 83
Omitted endnote
P.-G. de Gennes, Superconductivity of Metals and Alloys (W. A. Benjamin, Inc., New York, 1966), Chap. 7
Omitted endnote
W. A. Little and R. D. Parks, Phys. Rev. Letters 9, 9 (1962) R. D. Parks and W. A. Little, Phys. Rev. 133, A97 (1964)
R. P. Groff and R. D. Parks, Phys. Rev. 176, 567 (1968)
B. S. Deaver and W. M. Fairbank, Phys. Rev. Letters 7, 43 (1961) R. Doll and M. Näbauer, ibid. 7, 50 (1961)
([25])
Omitted endnote
Omitted endnote
R. Landauer and J. A. Swanson, Phys. Rev. 121, 1668 (1961)
J. S. Langer, Phys. Rev. Letters 21, 973 (1968)
A. Schmid, Physik Kondensienten Materie 5, 302 (1966)
E. Abrahams and T. Tsuneto, Phys. Rev. 152, 416 (1966) E. Abrahams and J. W. F. Woo, Phys. Letters 27A, 117 (1968)
D. E. McCumber and B. I. Halperin (to be published)
J. H. Davis, M. J. Skove, and E. P. Stillwell, Solid State Commun. 4, 597 (1966)
W. W. Webb, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 159
J. E. Lukens and J. M. Goodkind (private communication)
Omitted endnote
Omitted endnote
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965)

[c1] J. S. Langer and V. Ambegaokar, Phys. Rev. 164, 498 (1967)

[c2] W. W. Webb and R. J. Warburton, Phys. Rev. Letters 20, 461 (1968)

[c3] J. Franks, Acta Met. 6, 103 (1958) C. Herring and J. K. Galt, Phys. Rev. 85, 1060 (1952)

[c4] D. E. McCumber, Phys. Rev. 172, 427 (1968)

[c5] R. D. Parks, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 141

[c6] R. D. Parks and R. P. Groff, Phys. Rev. Letters 18, 342 (1967)

[c7] T. K. Hunt and J. E. Mercereau, Phys. Rev. Letters 18, 551 (1967)

[c8] R. P. Groff, S¨. Marčelja, W. E. Masker, and R. D. Parks, Phys. Rev. Letters 19, 1328 (1967)

[c9] J. E. Zimmerman and A. H. Silver, Phys. Rev. Letters 19, 14 (1967) A. H. Silver and J. E. Zimmerman, Phys. Rev. 157, 317 (1967)

[c10] J. E. Lukens and J. M. Goodkind, Phys. Rev. Letters 20, 1363 (1968)

[c11] J. S. Langer, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 83

[c12] Omitted endnote

[c13] P.-G. de Gennes, Superconductivity of Metals and Alloys (W. A. Benjamin, Inc., New York, 1966), Chap. 7

[c14] Omitted endnote

[c15] W. A. Little and R. D. Parks, Phys. Rev. Letters 9, 9 (1962) R. D. Parks and W. A. Little, Phys. Rev. 133, A97 (1964)

[c16] R. P. Groff and R. D. Parks, Phys. Rev. 176, 567 (1968)

[c17] B. S. Deaver and W. M. Fairbank, Phys. Rev. Letters 7, 43 (1961) R. Doll and M. Näbauer, ibid. 7, 50 (1961)

[c18] ([25])

[c19] Omitted endnote

[c20] Omitted endnote

[c21] R. Landauer and J. A. Swanson, Phys. Rev. 121, 1668 (1961)

[c22] J. S. Langer, Phys. Rev. Letters 21, 973 (1968)

[c23] A. Schmid, Physik Kondensienten Materie 5, 302 (1966)

[c24] E. Abrahams and T. Tsuneto, Phys. Rev. 152, 416 (1966) E. Abrahams and J. W. F. Woo, Phys. Letters 27A, 117 (1968)

[c25] D. E. McCumber and B. I. Halperin (to be published)

[c26] J. H. Davis, M. J. Skove, and E. P. Stillwell, Solid State Commun. 4, 597 (1966)

[c27] W. W. Webb, in Fluctuations in Superconductors, edited by W. S. Goree and F. Chilton (Stanford Research Institute, Menlo Park, Calif., 1968), p. 159

[c28] J. E. Lukens and J. M. Goodkind (private communication)

[c29] Omitted endnote

[c30] Omitted endnote

[c31] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press Inc., New York, 1965)

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Intrinsic Fluctuations in Superconducting Rings Containing One-Dimensional Weak Links

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