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 [7]. 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 [1, 2]. The recent observation of an oxygen-mass dependent penetration depth λ(0) in YBa2Cu3O6+x [1] and in La2−xSrxCuO4 [2] has raised the question whether this effect could be attributed to the breakdown of the Migdal approximation [3]. In fact, according to the classical MigdalEliashberg theory of superconductivity, the zero temperature penetration depth in the London limit and in the absence of magnetic impurities [4] is given by: