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

TL;DR

This paper proposes that high-temperature superconductivity in cuprates arises from a percolation transition of regions with varying local critical temperatures, explaining the complex phase diagram and experimental observations.

Contribution

It introduces a percolation-based model for the superconducting transition in cuprates, accounting for spatial inhomogeneity and local variations in critical temperature.

Findings

Reproduces the cuprate phase diagram using the percolation model.

Explains the inhomogeneous nature of superconductivity in cuprates.

Provides insights into experimental features like nanoscale charge variations.

Abstract

Several recent experiments have revealed that the charge density $\rho$ in a given compound (mostly underdoped) is intrinsic inhomogeneous with large nanoscale spatial variations. Therefore it is appropriate to define a local charge density $\rho(r)$. 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 $\Delta_0(r)$. 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