Self-Organized Networks and Lattice Effects in High Temperature Superconductors I: Lattice Softening

The self-organized dopant percolative filamentary model, entirely orbital in character (no fictive spins), explains chemical trends in superconductive transition temperatures Tc, assuming that Cooper pairs are formed near dopants because attractive electron-phonon interactions outweigh repulsive Coulomb interactions. According to rules previously used successfully for network glasses, the host networks are marginally stable mechanically. The high Tc's are caused by softening of the host network, enormously enhanced by large electron-phonon interactions at interlayer dopants for states near the Fermi energy. Background (in)homogeneities (pseudogap regions) produce novel percolative features in phase diagrams.