We show that the inclusion of effects beyond Migdal's limit in the electron-phonon interaction naturally leads to an isotope effect for the effective mass $m^{ *}$ of the charge carriers even much before reaching the polaron limit. This is the situation already considered in our approach to nonadiabatic superconductivity. Such a result provides a scenario different from the polaronic one for the interpretation of the recently observed isotope effect on $m^{ *}$ in YBa$_{ 2}$Cu$_{ 3}$O$_{ 6+x}$ and La$_{ 2-x}$Sr$_{ x}$CuO$_{ 4}$.
Categories: cond-mat.supr-con