We first argue that the collective behaviour of the Cooper pairs created by thermal fluctuations well above the superconducting transition temperature, T C , is dominated by the uncertainty principle which, in particular, leads to a welldefined temperature, T C , above which the superconducting coherence vanishes. On the grounds of the BCS approach, the corresponding reduced-temperature, ε C ≡ ln(T C /T C ), is estimated to be around 0.55, i.e., above T C ≃ 1.7 T C coherent Cooper pairs cannot exist. The implications of these proposals on the superfluid density are then examined using the Gaussian-Ginzburg-Landau approximation. Then we present new measurements of the thermal fluctuation effects on the electrical conductivity and on the magnetization in different lowand high-T C superconductors with different dopings which are in excellent agreement with these proposals and that demonstrate the universality of ε C . 74.20.-z Theories and models of superconducting state 74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.) 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)

By using high quality single crystals and epitaxial thin films, the in-plane paraconductivity in almost optimally doped YBa 2 Cu 3 O 7Ϫ␦ , with T c0 տ92 K, was determined well inside the so-called short-wavelength fluctuation regime, which corresponds to reduced temperatures, ⑀ϵln(T/T c0 ), above typically ⑀ϭ0.1. It is then shown that these data may be explained in terms of the Gaussian-Ginzburg-Landau approach for bilayered superconductors by introducing a total energy cutoff, instead of the momentum cutoff approximation always used until now. These results seem to confirm the absence of appreciable pseudogap effects on the in-plane resistivity in optimally doped YBa 2 Cu 3 O 7Ϫ␦ superconductors.

The in-plane resistivity has been measured in La 2Ϫx Sr x CuO 4 ͑LSCO͒ superconducting thin films of underdoped (xϭ0.10,0.12), optimally doped (xϭ0.15), and overdoped (xϭ0.20,0.25) compositions. These films were grown on (100)SrTiO 3 substrates, and have about 150 nm thickness. The in-plane conductivity induced by superconducting fluctuations above the superconducting transition ͑the so-called in-plane paraconductivity ⌬ ab ) was extracted from these data in the reduced-temperature range 10 Ϫ2 Շϵln(T/T c )Շ1. This ⌬ ab () was then analyzed in terms of the mean-field-like Gaussian-Ginzburg-Landau ͑GGL͒ approach extended to the high-region by means of the introduction of a total-energy cutoff, which takes into account both the kinetic energy and the quantum localization energy of each fluctuating mode. The obtained GGL coherence length amplitude in the c direction, c (0), is constant for 0.10рxр0.15 ͓ c (0)Ӎ0.9 Å͔, and decreases with increasing x in the overdoped range ͓ c (0)Ӎ0.5 Å for xϭ0.20 and c (0)ϳ0 Å for xϭ0.25]. These results strongly suggest, therefore, that the superconducting fluctuations in underdoped and overdoped LSCO thin films may still be described, as in the optimally doped cuprates, in terms of the extended GGL approach; the main effect of doping is simply to change the fluctuations' dimensionality by varying the transversal superconducting coherence length amplitude. In contrast, the total-energy cutoff amplitude c remains unchanged well within the experimental uncertainties. Our results strongly suggest that at all temperatures above T c , including the high reduced-temperature region, doping mainly affects the normal-state properties in LSCO thin films and that its influence on the superconducting fluctuations is relatively moderate; even in the high-region, the in-plane paraconductivity is found to be independent of the opening of a pseudogap in the normal state of the underdoped films. We expect this last conclusion to be independent of the structural details of our films, i.e., applicable also to bulk samples.

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