Microscopic model for the isotope effect in the high-Tcoxides

An unconventional microscopic mechanism relating ${\mathit{T}}_{\mathit{c}}$ and the isotope substitution for the doped superconductors such as the high-${\mathit{T}}_{\mathit{c}}$ oxides is proposed. Strong nonadiabaticity, when it is impossible, strictly speaking, to separate fully the nuclear and electronic degrees of freedom, leads to a peculiar dependence of the carrier concentration n on the ionic mass M. This case corresponds, for example, to the isotopic substitution of the axial oxygen in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$. Because of the dependence of ${\mathit{T}}_{\mathit{c}}$ on n, this leads to the dependence of ${\mathit{T}}_{\mathit{c}}$ on M, that is to the isotope effect. The minimum value of the isotope coefficient corresponds to ${\mathit{T}}_{\mathit{c}}$=${\mathit{T}}_{\mathit{c}}^{\max }$.