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

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

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