In order to unveil the origin of the gapless properties of cuprate superconductors, we study the low temperature dependence of the magnetic penetration depth λ in: a) conventional NbN superconducting films with granular and epitaxial microstructure; b) single crystals of La 2-x Sr x CuO 4, Bi 2 Sr 2 CaCu 2 O 8 (BSCCO) and YBa 2 Cu 3 O 6+x at various doping levels ranging from the under- to the overdoped regimes. The measurements are performed by using a novel single-coil technique achieving 10 pm resolution. Our experimental results are as follows. a) The granular NbN films exhibit a linear low-temperature dependence of λ similar to the dependence reported earlier in cuprates. In the epitaxial NbN films, we find the characteristic exponential behaviour of conventional s-wave superconductors. b) In all single crystals of cuprates, the data confirm the linear dependence of λ ab reported earlier. In BSCCO, we find that the slope d λ ab / dT is rapidly increasing as doping decreases. As to a), our results give evidence for a gapless behaviour in conventional s-wave superconductors induced by a granular microstructure. As to b), our analysis indicates that a simple d-wave model accounts for the experimental slope values only in the optimally and over-doped samples. In the underdoped samples, the d-wave model underestimates the large slope values observed experimentally. Such large values are rather consistent with a simple model of thermodynamic phase fluctuations suited for metals with reduced dimensionality and low carrier density, as in cuprates. We argue that this fluctuation model also accounts for the linear dependence of λ found in our granular NbN films. We discuss possible mechanisms associated with the existence of weak links across the grains, which would favour thermally activated phase fluctuations of the gap in this conventional superconductor. Finally, we put forward the hypothesis that a similar phenomenon may occur in cuprates because of the intrinsic granularity associated with phase-separated metallic and insulating regions in the superconducting ab-plane.
d-wave model for microwave response of high-Tcsuperconductors