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.

A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg-Landau equationAn approach to the Ginzburg-Landau problem for superconducting regular polygons is developed making use of an analytical gauge transformation for the vector potential A which gives A n = 0 for the normal component along the boundary line of different symmetric polygons. As a result the corresponding linearized Ginzburg-Landau equation reduces to an eigenvalue problem in the basis set of functions obeying Neumann boundary condition. Such basis sets are found analytically for several symmetric structures. The proposed approach allows for accurate calculations of the order parameter distributions at low calculational cost ͑small basis sets͒ for moderate applied magnetic fields. This is illustrated by considering the nucleation of superconductivity in squares, equilateral triangles and rectangles, where vortex patterns containing antivortices are obtained on the T c -H phase boundary. The calculated phase boundaries are compared with the experimental T c ͑H͒ curves measured for squares, triangles, disks, rectangles, and loops. The stability of the symmetry consistent solutions against small deviations from the phase boundary line deep into the superconducting state is investigated by considering the full Ginzburg-Landau functional. It is shown that below the nucleation temperature symmetry-switching or symmetry-breaking phase transitions can take place. The symmetry-breaking phase transition has the same structure as the pseudo-Jahn-Teller instability of high symmetry nuclear configurations in molecules. The existence of these transitions is predicted to be strongly dependent on the size of the samples.

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.

For the first time for a cuprate superconductor, measurements performed above T(c) in high quality grain aligned La1.9Sr0.1CuO4 samples have allowed the observation of the thermal fluctuation induced diamagnetism well inside the finite-magnetic-field fluctuation regime. These results may be explained in terms of the Gaussian Ginzburg-Landau approach for layered superconductors, but only if the finite field contributions are estimated by taking off the short-wavelength fluctuations.

The effects induced on the magnetization by coherent fluctuating Cooper pairs in the normal state have been measured in Pb 1−x In x alloys up to high magnetic fields, of amplitudes above H C2 (0), the upper critical field extrapolated to T =0 K. Our results show that in dirty alloys these superconducting fluctuation effects are, in the entire H − T phase diagram above H C2 (T ), independent of the amount of impurities and that they vanish when H ∼ 1.1H C2 (0). These striking results are consistent with a phenomenological estimate that takes into account the limits imposed by the uncertainty principle to the shrinkage, when H increases, of the superconducting wave function.