Self-organized networks and lattice effects in high-temperature superconductors

The self-organized dopant percolative filamentary model, entirely orbital in character (no fictive spins), explains quantitatively and uniquely chemical trends in superconductive transition temperatures Tc, assuming that Cooper pairs are formed near soft dopants because there attractive electron-phonon pairing 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 even softer interlayer dopants for states near the Fermi energy. Background inhomogeneities (antiferroelectric pseudogap regions) produce percolative ``hydrodynamic'' features in phase diagrams. The model is especially successful in describing the appearance of giant magnetic vortex ``precursive'' effects at temperatures ~2Tc far above the superconductive transition temperature Tc. The anomalous precursive temperature-dependent strains observed by extended x-ray-absorption fine structure are associated with relaxation of filamentary ends. Abrupt transitions at optimal doping are observed in time-resolved picosecond relaxation spectroscopy at 1.50.3em0exeV, and these are explained as well using no new assumptions and no adjustable parameters. The theory resolves the mystery of the vanishing isotope effect at optimal doping. Both broad and detailed features of global atomic-scale tunneling characteristics reported in 2007 in underdoped cuprates are in excellent agreement with the lateral and/or vertical zigzag filamentary model discussed in 1990.