The Resistive Transition of Inhomogeneous Superconductors : Effects of “Mild” Granularity, Dimensionality, Gaussian Fluctuations and Critical Behaviour

  • P. Peyral
  • C. Lebeau
  • J. Rosenblatt
  • A. Raboutou
Part of the NATO ASI Series book series (NSSB, volume 222)


Early studies of granular superconducting films1,2 showed that as long as the electronic mean-free-path ℓ was limited by the grain size a, little or no effect on the superconducting properties could be observed, while the normal-state-resistivity ρN was metallic, that is, dρN/dT > 0. Only when the apparent ℓ < a and dρN/dT < 0, indicating that insulating tunnelling barriers developed between grains, the critical temperature decreased and the resistive transition broadened dramatically1. We have shown that this broadening could be described in the case of weakly coupled grains with a ≫ ξ(T) (the Ginzburg-Landau coherence length) as a double transition3:the grains first become individually superconducting at a temperature Tcs and then the complex vectors representing the superconducting order parameter in each grain reach a coherent state when they become phase-ordered in the complex plane at a temperature Tc < Tcs. This is just the analogue of a paramagnetic-ferromagnetic XY phase transition4, where the phase- dependent intergranular coupling energy J ≃ kBTc plays the role of the exchange integral. Granularity becomes relevant in the superconducting state when J < Ec, the single-grain condensation energy in the normal state, when ρN ≫ ρGN, where ρb and ρGN are the barrier and grain contributions to ρN = ρb + ρGN.


Coherent State Resistive Transition Superconducting Order Parameter Excess Conductivity Condensation Energy 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • P. Peyral
    • 1
  • C. Lebeau
    • 1
  • J. Rosenblatt
    • 1
  • A. Raboutou
    • 1
  1. 1.Laboratoire de Physique des SolidesURA 786 au CNRS INSARennes CedexFrance

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