Is the Superconductiong State for the Cuprates Reached Through a Percolation Transition?

Abstract

Several recent experiments have revealed that the charge density $ρ$ in a given compound (mostly underdoped) is intrinsic inhomogeneous with large nanoscale spatial variations. Therefore it is appropriate to define a local charge density $ρ(r)$. These differences in the local charge concentration yield insulator and metallic regions, either in an intrinsic granular or in a stripe morphology. In the metallic region, the inhomogeneous charge density produces spatial or local distributions of superconducting critical temperatures $T_c(r)$ and zero temperature gap $Δ_0(r)$. We propose that the superconducting phase in high-$T_c$ oxides is reached when the temperature reachs a value which superconduction regions with different critical temperatures percolates. We show also that this novel approach is able to reproduce the phase diagram for a family of cuprates and provides new insights on several experimental features of high-$T_c$ oxides