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Fractal vortices in disordered superconductors

Author

Listed:
  • Raboutou, A.
  • Peyral, P.
  • Lebeau, C.
  • Rosenblatt, J.
  • Burin, J.P.
  • Fouad, Y.

Abstract

We measure the low-frequency magnetic response χ = χ′ + iχ″ of halogenated ceramics YBa2Cu3O7−δFx as functions of x, AC field amplitude H0 and temperature T. The field of first flux penetration displays scaling behaviour: H1(x, T) = H1(x, 0) (1 − T/Tc)ζ, with Tc the coherence temperature and ζ = 2.7 ± 0.2; in all cases H1 ⪢ Hc1 expected for the ideal material. A model where deviations from stoichiometry are assumed to result in local critical temperatures Tc(r), is described. Superconductivity is due to regions where T< Tc(r) with concentration p(T). The coherence temperature is defined by p(Tc) = pc, the percolation threshold. Critical exponents appear to be related to percolation exponents, in particular ν = 2νp/3βp≅ 1.33, in agreement with the experimental value found in granular superconductors. Expressions are found for the magnetic fields observed in Euclidean space while being due to currents restricted to fractal percolation clusters. The free energy of the resulting fractal vortices accounts for the experimental value of the exponent in the temperature dependence of H1(T).

Suggested Citation

  • Raboutou, A. & Peyral, P. & Lebeau, C. & Rosenblatt, J. & Burin, J.P. & Fouad, Y., 1994. "Fractal vortices in disordered superconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(1), pages 271-279.
    • Handle: RePEc:eee:phsmap:v:207:y:1994:i:1:p:271-279
    DOI: 10.1016/0378-4371(94)90384-0
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    References listed on IDEAS

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    1. Gianelli, A. & Giovannella, C., 1990. "Non-Debye relaxation and dynamical scaling in high-Tc granular superconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 277-282.
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    Cited by:

    1. Renat T. Sibatov, 2020. "Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids," Mathematics, MDPI, vol. 8(11), pages 1-14, November.

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