A quantum phase transition driven by the electron lattice interaction gives high Tc superconductivity

We identify for the first time the quantum phase transition (QPT) as a function of the electron lattice interaction for charge localization in stripes with local lattice distortions in cuprate perovskites at metallic densities. The electron lattice interaction lambda(eta) is triggered at the localization limit by the strain eta of the CuO2 plane due to the chemical pressure generated by the mismatch between the copper oxide and the rocksalt layers. The strain of the CuO2 plane has been directly measured by Cu K-edge EXAFS. The critical point for the ch;uge localization in striped lattice domains coexisting with itinerant carriers is at eta (c)=0.04 +/-0.005 and delta (c)=0.16 +/-0.03. We report a 2D plot T-c (delta,eta) for the doped perovskites, where delta is the doping. The plot T-c(eta), for delta =constant, shows the highest T-c at the critical point eta (c)=0.04 +/-0.01. The attractive pseudo Jahn-Teller (pJT) interaction and the particular critical charge and spin fluctuations driven by critical ordering of cooperative pJT local lattice distortions, forming a superlattice of quantum stripes tuned at a 'shape resonance' near this quantum critical point, provide a possible solution for two long standing mysteries: the phase diagram and the pairing mechanism in cuprate superconducters.