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 (Phys. Rev. Lett., 75 (1995) 1158). 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., Phys. Rev. B, 51 (1995) 16487 and Nature, 385 (1997) 236).