Isotope effect in the pseudogap state of high-temperature copper oxide superconductors

We study cuprates within the dynamical cluster approximation and find that the pseudogap displays an isotope effect of the same sign as observed experimentally. Notwithstanding the nonphononic origin of the pseudogap, the interplay between electronic repulsion and retarded phonon-mediated attraction gives rise to an isotope dependence of the antinodal spectra. Due to the strong momentum differentiation, such an interplay is highly nontrivial and leads to the simultaneous presence of heavier quasiparticles along the nodal direction. We predict an isotope effect in electron-doped materials.