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 o f the magnetic penetration depth A in (1) superconducting NbN films grown o n R-plane sapphire and MgO substrates and (2) Bi2212 single crystals with d ifferent doping levels ranging from under- to over-doping. The NbN films di splay textured or epitaxial microstructure depending on growth conditions. The thermally activated dependence of lambda (T) characteristic of conventi onal s-wave superconductors was found only in the epitaxial or thin texture d NbN films. All thick textured films exhibit below 4 K a linear dependence Delta lambda similar to T characteristic of a gapless superconducting stat e. This is quantitatively explained by a model of granularity-induced therm al 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 pronounce d 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 bo th under- and over-doping. These values are quantitatively explained by the same model of phase fluctuations adopted for the textured NbN films, in sp ite of the difference between these two superconducting systems. (C) 2001 P ublished by Elsevier Science B.V.