Granular superconductivity in the cuprates evinced by finite size effects in the specific heat and London penetration depths

We review and refine the finite size scaling analysis of specific heat and London penetration depths data of cuprate superconductors and compare it to the analysis of specific heat measurements near the superfluid transition of 4He confined to 1mum^3 cylindrical boxes. This system crosses from 3D to 0D behavior near the transition. This has a marked effect on the specific heat as seen by a pronounced rounding of the maximum and a shift to a temperature lower than the transition temperature of the bulk system. The region in between the 3D to 0D crossover uncovers the contributions from the surface and the edges of the cylindrical boxes. Our finite size scaling analysis of the specific heat and London penetration depth of high quality Y-123 and Bi-2212 single crystals uncover essentially the same crossover phenomena, including evidence for surface and edge contributions. These uncovers granular superconductivity in the samples considered here.