  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.
