Gapless state in low- and high-T-c superconductors: evidence for thermal phase fluctuations

We have carried out a comparative study of the low-temperature dependence of the magnetic penetration depth A in (1) superconducting NbN films grown on R-plane sapphire and MgO substrates and (2) Bi2212 single crystals with different doping levels ranging from under- to over-doping. The NbN films display textured or epitaxial microstructure depending on growth conditions. The thermally activated dependence of lambda (T) characteristic of conventional s-wave superconductors was found only in the epitaxial or thin textured NbN films. All thick textured films exhibit below 4 K a linear dependence Delta lambda similar to T characteristic of a gapless superconducting state. This is quantitatively explained by a model of granularity-induced thermal phase fluctuations of the order parameter. As for Bi2212, we have found in all crystals a linear low-temperature dependence Delta lambda similar to T in the ab-plane. The slope Delta lambda (ab)/DeltaT displays a pronounced minimum similar to8 Angstrom /K at optimum doping. This value is in good agreement with the d-wave model proposed for cuprates. However, this model fails to account for the large slope values > 40 Angstrom /K observed at both under- and over-doping. These values are quantitatively explained by the same model of phase fluctuations adopted for the textured NbN films, in spite of the difference between these two superconducting systems. (C) 2001 Published by Elsevier Science B.V.