Isotope effect on m* in high-Tc materials due to the breakdown of Migdal's theorem

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 YBa2Cu3O6+x and La2-xSrxCuO4 (Zhao et al., (1995) and (1997)). (orig.)