Nonlinear Electron-lattice Coupling Solution to High Temperature Superconductivity in Cuprates

Resolving the High Temperature Superconductivity problem requires understanding both pseudogap and superconducting phenomenologies. Here we present a model, the Fluctuating Bond Model (FBM) based on strong, local, nonlinear electron-lattice coupling and now including long range Coulomb interactions (LRCI), which can claim to achieve this requirement. We summarize the results on the pseudogap temperature scale $T^*$ and pseudogap doping dependence, relating them to low temperature STM experiments (``C$4$ symmetry breaking'') and to ARPES data (``arcing'' of the Fermi surface). We also summarize results on the doping dependence of the superconducting $T_c$ and the isotope shift. We conclude with a list of challenges to be met by theory. \\[4pt] D.M.Newns and C.C. Tsuei, Nature Physics \textbf{3}, 184 (2007).