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In cuprate superconductors, a pronounced maximum of superconducting Tc isobserved in compounds that have an in-plane Cu-O distance close to ~1.92Angstroms. On the other hand, direct measurements of the electron-phononcoupling lambda as a function of Cu-O distance show a clear linear correlation,implying that Tc is a strongly non-linear function of lambda. Conventionalsuperconductivity theories based on the electron-phonon interaction predict amonotonic dependence of Tc on electron phonon coupling constant, which makesthem incompatible with the observed behaviour. The observed cross-overbehaviour as a function of lambda suggests that Tc occurs at the cross-overfrom weak to strong coupling, which is also associated with the onset ofcarrier localization. A coexistence, with a dynamical exchange of localized anditinerant carriers in a two-component superconductivity scenario are inagreement with the observed anomalous behavior and are suggested to be the keyto understanding the mechanism for achieving high Tc.

Why does maximum Tc occur at the cross-over from weak to strong electron-phonon coupling in high temperature superconductors?