Isotope effect on the superconducting critical temperature of cuprates in the presence of charge order

Using the large-N limit of the t–J model and also allowing for phonons and the electron–phonon interaction, we study the isotope effect α for coupling constants appropriate for YB2C3Oy. We find that α has a minimum at optimal doping and increases strongly (slightly) towards the underdoped (overdoped) region. Using values for the electron–phonon interaction from the local density approximation we get good agreement for α as a function of Tc and doping δ with recent experimental data in YB2C3Oy. Our results strongly suggest that the large increase of α in the underdoped region is (a) caused by the shift of electronic spectral density from low to high energies associated with a competing phase (in our case a charge density wave) and the formation of a gap, and (b) compatible with the small electron–phonon coupling constants obtained from the local density approximation. We propose a similar explanation for the anomalous behavior of α in Sr-doped La2CuO4 near the doping 1/8.