Filamentary theory of cuprate superconductivity phase diagram and giant electron-phonon interactions

Both the mathematical foundations and the connections with experiment of the filamentary model of high temperature cuprate superconductivity have improved greatly in the last two years. The filamentary paths are variationally optimized conductivity paths for electrons near the Fermi energy in the normal state. These paths, and the electronic basis states connected with them, account not only for the anomalously linear temperature dependence of the normal-state resistivities and Hall numbers, but also for the astonishing compositional coincidence of these linearities with the maximum in T-c. These anomalies appear to coincide with the metal-insulator transition. To understand the latter, the author has, for the first time, solved its simplest case, which occurs in semiconductor impurity bands (such as Si:P). There a careful analysis of the experimental data (some of which have been "lost" for twenty years!) uncovered a phase diagram with a new intermediate "X" phase which has properties very similar to those of the cuprate "non-Fermi liquid" normal state. In the X phase the dopant-electron-phonon interaction is similar to 25 times larger than in normal metallic Fermi Liquids. Together with the phase-diagram similarity this large factor strongly suggests that the filamentary model is the correct starting point for a non-effective medium percolative model of high temperature cuprate superconductivity.