Percolation, fractal behavior, and high-Tc superconductivity

Hole suppliers like Sr in doped La2CuO4 are mainly randomly distributed. Assuming that the holes are dislocated over a few lattice constants away from the Sr atom, the conducting areas form randomly distributed circles in the CuO2 layer planes. Conductivity and also superconductivity can occur only when these circles touch each other and form percolation clusters. Mobile holes are accompanied by diffusing d-electrons. Their spin direction is no longer localized on distinct places, and antiferromagnetism breaks down. The phase diagram of high-T-c superconductors is discussed on the basis of a modified continuum percolation model for which the centers of each circle are located on lattice points. The inhomogeneities due to the random hole distributions lead to broad peaks instead of sharp singularities in the static and dynamic response functions.