Abstract
Recent experiments on granular films have shown an apparently universal maximum normal state sheet resistance of around 6.5 kΩ above which superconductivity cannot be established. A possible explanation for this phenomenon is presented which is based on the competition between quantum fluctuations in the phase of the superconducting order parameter and dissipative effects. The films are modelled by locally superconducting grains coupled through Josephson junctions. Quantum fluctuations in the phases of individual grains may lead to a state in which the Cooper pair number rather than its conjugate phase is a good quantum number and superconductivity is destroyed. Dissipative effects tend to suppress these fluctuations and lead to the appearance of a new type of superconducting state possessing only short range phase coherence. This occurs for normal state resistances smaller than the quantum unit h/4e 2=6.5 kΩ, in agreement with the experimentally observed threshold.
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References
A.I. Shalnikov, Zh. Eksper. i Teor. Fiz. 10, 630 (1940)
W. Buckel, and R. Hilsch, Z. Phys. 138, 109 (1954)
See e.g. the review by W.J. Skocpol and M. Tinkham, in: Rep. Prog. Phys.38, 1049 (1975)
See e.g. the review by J.E. Mooij, in: Percolation, Localization and Superconductivity ed. by A.M. Goldman, and S.A. Wolf (Plenum Press, New York 1984), p. 325
H. Ebisawa, H. Fukuyama, and S. Maekawa, J. Phys. Soc. Jpn. 54, 2257 (1985)
M. Strongin, R.S. Thompson, O.F. Kammerer, and J.E. Crow, Phys. Rev. B1, 1078 (1970)
B.G. Orr, H.M. Jaeger, and A.M. Goldman, Phys. Rev. B32, 7586 (1985)
B.G. Orr, H.M. Jaeger, A.M. Goldman, and C.G. Kuper, Phys. Rev. Letters 56, 378 (1986)
H.M. Jaeger, D.B. Haviland, A.M. Goldman, and B.G. Orr, Phys. Rev. B34, 4920 (1986)
H.M. Jaeger, D.B. Haviland, B.G. Orr, and A.M. Goldman, Preprint, University of Minnesota (1988)
Note that in a two dimensional film the resistance is independent of the sample dimensions (assuming isotropy and a square geometry for simplicity). This peculiar scale invariance allows us to relate the local tunnel resistances between the grains to the overall film resistance.
R.C. Dynes, J.P. Garno, and J.M. Rowell, Phys. Rev. Letters 40, 479 (1978)
S. Kobayashi, Y. Tada, and W. Sasaki, J. Phys. Soc. Jpn. 49, 2075 (1980)
A.F. Hebard, and M.A. Paalanen, Phys. Rev. B30, 4063 (1984)
S. Kobayashi, and F. Komori, J. Phys. Soc. Jpn. 57, 1884 (1988)
V. Ambegaokar, B.I. Halperin, and J.S. Langer, Phys. Rev. B4, 2612 (1971)
C.G. Neugebauer, and M.B. Webb, J. Appl. Phys. 33, 74 (1962)
B. Abeles, P. Sheng, M.D. Coutts, and Y. Arie, Adv. Phys. 24, 407 (1975)
For a recent discussion see: R. Németh, and B. Mühlschlegel, Z. Phys. B70, 159 (1988)
Y. Imry, and M. Strongin, Phys. Rev. B24, 6353 (1981)
R. Brown, and E. Šimánek, Phys. Rev. B34, 2957 (1986)
B. Mühlschlegel, D.J. Scalapino, and R. Denton, Phys. Rev. B6, 1767 (1972)
G. Deutscher, Y. Imry, and L. Gunther, Phys. Rev. B10, 4598 (1974)
L.J. Geerligs, and J.E. Mooij, Physica B152, 212 (1988)
For a recent review see: P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987)
J.M. Graybeal, and M.R. Beasley, Phys. Rev. B29, 4167 (1984)
B. Abeles, Phys. Rev. B15, 2828 (1977)
K.B. Efetov, Sov. Phys. JETP 51, 1015 (1980)
E. Šimánek, Solid State Comm. 31, 419 (1979)
S. Doniach, Phys. Rev. B24, 5063 (1981)
P. Fazekas, B. Mühlschlegel, and M. Schröter, Z. Phys. B57, 193 (1984)
A.O. Caldeira, and A.J. Leggett, Ann. Phys. 149, 374 (1983)
W. Zwerger, Europhys. Letters, in print (1989)
A. Schmid, Phys. Rev. Letters 51, 1506 (1983)
M.P.A. Fisher, and W. Zwerger, Phys. Rev. B32, 6190 (1985)
W. Zwerger, Phys. Rev. B35, 4737 (1987)
S.T. Chui, and J.D. Weeks, Phys. Rev. B14, 4978 (1976)
J.A. Hertz, Phys. Rev. B14, 1165 (1976)
R.M. Bradley, and S. Doniach, Phys. Rev. B30, 1138 (1984)
M.P.A. Fisher, Phys. Rev. B36, 1917 (1987)
S. Chakravarty, S. Kivelson, G. Zimanyi, and B.I. Halperin, Phys. Rev. B35, 7256 (1987)
A. Kampf, and G. Schön, Phys. Rev. B36, 3651 (1987)
A.D. Zaikin, Physica B152, 251 (1988)
R.A. Ferrell, and B. Mirhashem, Phys.Rev. B37, 648 (1988)
S. Chakravarty, G.L. Ingold, S. Kivelson, and G. Zimanyi, Phys. Rev. B37, 3283 (1988)
J.S. Langer, and V. Ambegaokar, Phys. Rev. 164, 498 (1967)
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH
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Zwerger, W. (1989). Quantum effects and the onset of superconductivity in granular films. In: Rössler, U. (eds) Festkörperprobleme 29. Advances in Solid State Physics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108005
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DOI: https://doi.org/10.1007/BFb0108005
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