Manifestation of percolation in high temperature superconductivity

Emergent advanced electronic and magnetic functionalities in novel materials appear in systems with a complex lattice structure. The key point is understanding the intrinsic effect of lattice fluctuations on the relevant electronic features in the range of 10-100 meV near the Fermi level in new materials which is needed to develop advanced quantum nano-devices. This requires the control of structural inhomogeneity at multiple scales. Here we report some of the known advances in the field of percolative superconductivity. The necessity of the review is based on the growing consensus that the lack of an understanding of high temperature superconductivity is due to the few information on lattice fluctuations. In particular they could control the pseudo-gap phase, the electronic duality of holes in Fermi arcs and electrons in small Fermi pockets, multiple condensates in different points of the k-space. Moreover the emerging lattice granularity in cuprates shifts the search for the superconducting mechanism from a homogeneous superconductivity to a percolative superconductivity, therefore it is the scope of this review to provide further data to this kind of research.