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.)

The superconducting fluctuations well inside the normal state of Fe-based superconductors were studied through measurements of the in-plane paraconductivity and magnetoconductivity in high quality BaFe 2−x Ni x As 2 crystals with doping levels from the optimal level (x = 0.10) up to highly overdoped (x = 0.20). These measurements, performed in magnetic fields up to 9 T perpendicular to the ab (Fe) layers, allowed a reliable check of the applicability to iron-based superconductors of Ginzburg-Landau approaches for 3D anisotropic compounds, even at high reduced temperatures and magnetic fields. Our results also allowed us to gain valuable insight into the dependence on the doping level of some central superconducting parameters (coherence lengths and anisotropy factor).

By using a Pb-18 at. % In alloy, the fluctuation induced diamagnetism was measured in the zero magnetic field limit, never observed until now in a low-T(C) superconductor. This allows us to disentangle the dynamic and the nonlocal electrodynamic effects from the short-wavelength fluctuation effects. The latter may be explained on the grounds of the Gaussian-Ginzburg-Landau approach by introducing a total energy cutoff in the fluctuation spectrum, which strongly suggests the existence of a well-defined temperature in the normal state above which all fluctuating modes vanish. This conclusion may also have implications when describing the superconducting state formation of the high-T(C) cuprates.

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.

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The inhomogeneities inherent to the random distribution of Sr dopants in La2−xSrxCuO4 superconductors are probed by measuring the x-ray diffraction linewidths and the Meissner transition widths, and then consistently explained on the grounds of a simple model in which the local Sr content is calculated by averaging over distances close to the in-plane electronic mean free path. By taking into account these intrinsic bulk inhomogeneities with long characteristic lengths (much larger than the superconducting coherence length amplitudes), the precursor diamagnetism measured above Tc, a fingerprint of the superconducting transition own nature, is then explained for all doping levels in terms of the conventional Gaussian-Ginzburg-Landau approach for layered superconductors. These results also suggest that the electronic inhomogeneities observed in the normal state by using surface probes overestimate the ones in the bulk.

By using two randomly oriented polycrystalline YBa2Cu3O7 − δ samples with masses as big as 0.63 g and 0.90 g, but almost optimally doped (Tc0 ≃ 90.8 K and 92.0 K) and with excellent stoichiometric homogeneity, the in-plane fluctuation-induced diamagnetism was determined, for the first time in any superconductor, well inside the so-called short wavelength regime in the zero-magnetic-field limit, which corresponds to reduced temperatures, ϵ ≡ ln (T/Tc0), above typically ϵ = 0.1. It is then shown that these measurements may be explained in terms of the Schmidt limit of the Gaussian-Ginzburg-Landau approach for bilayered superconductors by introducing a total-energy cut-off in the fluctuation spectrum.

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