Evidence for granularity, anisotropy and lattice distortions in cuprate superconductors and their implications

Granularity, anisotropy, local lattice distortions and their dependence on dopant concentration appear to be present in all cuprate superconductors, interwoven with the microscopic mechanisms responsible for superconductivity. Here we review anisotropy and penetration depth measurements to reassess the evidence for granularity, as revealed by the notorious rounded phase transition, the evidence for the three dimensional nature of superconductivity, uncovered by the doping dependence of transition temperature and anisotropy, and to reassess the relevance of the electron-lattice coupling, emerging from the oxygen isotope effects.