Finite-size effect in Bi 2 Sr 2 CaCu 2 O 8+δ and YBa 2 Cu 3 O 6.7 probed by the in-plane and out-of-plane penetration depths

We report on a systematic finite-size scaling analysis of in-plane penetration depth data taken on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ epitaxially grown films and single crystals, and of in-plane and out-of-plane data taken on ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.7}$ aligned powder. It is shown that the tails in temperature dependence of the penetration depths, appearing around the transition temperature, are fully consistent with a finite-size effect. This uncovers the granular nature of these cuprates, consisting of superconducting homogeneous domains of nanoscale extent, embedded in a nonsuperconducting matrix.