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.

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The in-plane diamagnetism around the Meissner transition was measured in a Tl2Ba2Ca2Cu3O10 single crystal of high chemical and structural quality, which minimizes the inhomogeneity and disorder rounding effects on the magnetization. When analyzed quantitatively and consistently above and below the transition in terms of the Ginzburg-Landau (GL) approach with fluctuations of Cooper pairs and vortices, these data provide a further confirmation that the observed Meissner transition is a conventional GL superconducting transition in a homogeneous layered superconductor.

The fluctuation-induced diamagnetism ∆M , associated with the presence of precursor Cooper pairs in the normal state, has been measured in lanthanum with dilute magnetic (Pr) and nonmagnetic (Lu) impurities. It is found that while for pure La and La-Lu alloys ∆M agrees, as expected, with the theoretical predictions, it is much larger for La-Pr alloys (around a factor 5 for La-2 at.%Pr). These results suggest the existence of an indirect contribution to ∆M arising from the interaction between fluctuating Cooper pairs and magnetic impurities.

In a recent Letter[1], Wang et al. claim that "the magnetization results above T C distinguish M from conventional amplitude fluctuations and strongly support the vortex scenario for the loss of phase coherence at T C ." However, we will present here some examples for T > T C that show that the data of Ref.[1] may be explained on the grounds of the conventional Ginzburg-Landau (GL) scenario. We have checked that this conclusion applies also to both the temperature and the magnetic field dependende of M below T C .Note first that the absence on non-local electrodynamic effects on the fluctuation magnetization M ′ measured in Ref.[1] just confirms earlier results (see, e.g., Refs.[2,3]). A similar absence was also observed in dirty low-T C superconductors[4] and therefore, contrary to the claims of Wang et al., it does not provide a "first evidence" of unconventional fluctuations.To estimate M ′ (T, H) above but not too close to T C we may use the GL theory with Gaussian fluctuations (GGL approach) in the 2D limit[5],