Abstract
The displacement correlation function introduced by Larkin and Ovchinnikov for pinned flux lines in a superconducting layer is evaluated explicitly in order to study the thickness dependence. Expressions for the transverse and longitudinal correlation lengthsR c andL care derived and a criterion for the crossover from two- to three-dimensional collective pinning is obtained. Using these expressions, computations are carried out for amorphous superconductors.L cturns out to drop exponentially fast in three dimensions, whileR cchanges gradually through the crossover remaining close to its 2D value. The explicit thickness dependence is logarithmic, so that the pure 3D case is only accessible in a very limited experimental regime.
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References
P. H. Kes and C. C. Tsuei,Phys. Rev. B 28, 5126 (1983);Phys. Rev. Lett. 47, 1930 (1981).
N. Toyota, A. Inoue, T. Fukase, and T. Masumoto,J. Low Temp. Phys. 55, 393 (1984).
S. Yoshizumi, W. L. Carter, and T. H. Geballe,J. Non-Cryst. Solids 61/62, 598 (1984).
E. J. Osquiguil, V. L. P. Frank, and F. de la Cruz,Solid State Commun. 55, 227 (1985).
E. J. Kramer,J. Nucl. Mater. 72, 5 (1978).
A. I. Larkin and Yu. N. Ovchinnikov,J. Low Temp. Phys. 34, 409 (1979).
R. Wördenweber and P. H. Kes, Physica135B, 136 (1985).
E. N. Martinez, V. L. P. Frank, E. J. Osquiguil, and F. de la Cruz,Solid State Commun. 60, 151 (1986).
R. Wördenweber and P. H. Kes,Phys. Rev. B 34, 494 (1986).
R. Wördenweber, P. H. Kes, and C. C. Tsuei,Phys. Rev. B 33, 3172 (1986).
S. J. Mullock and J. E. Evetts,J. Appl. Phys. 57, 2588 (1985).
H. R. Kerchner, D. K. Christen, C. E. Klabunde, S. T. Sekula, and R. R. Coltman,Phys. Rev. B 27, 5467 (1983).
R. Meier-Hirmer, H. Küpfer, and H. Scheuer,Phys. Rev. B 31, 183 (1985).
G. P. van der Meij and P. H. Kes,Phys. Rev. B 29, 6233 (1984).
E. H. Brandt,Phys. Rev. Lett.,57, 1347 (1986).
E. H. Brandt,J. Low Temp. Phys.,64, 375 (1986).
E. H. Brandt,J. Low Temp. Phys. 26, 709;26, 735;28, 263;28, 291 (1977).
E. H. Brandt,J. Low Temp. Phys. 53, 41;53, 71 (1983);Phys. Rev. Lett. 50, 1599 (1983).
I. S. Gradshteyn and I. M. Ryznick,Tables of Integrals, Series and Products (Academic Press, New York, 1965).
H. R. Kerchner,J. Low Temp. Phys. 50, 335 (1983).
M. G. Blamire and J. E. Evetts,Phys. Rev. B 33, 5131 (1986); J. Clem and A. Perez-Gonzales,Phys. Rev. B 33, 1601 (1986); see also T. Matsushita, K. Yamafuji, and F. Irie, eds.,Proceedings of International Symposium on Flux Pinning and Electromagnetic Properties in Superconductors, Fukuoka, 1985.
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Kes, P.H., Wördenweber, R. Computations on the dimensional crossover in collective pinning. J Low Temp Phys 67, 1–15 (1987). https://doi.org/10.1007/BF01070646
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DOI: https://doi.org/10.1007/BF01070646