Isotopic shift in angle-resolved photoemission spectra of Bi2Sr2CaCu2O8 due to quadratic electron–phonon coupling

In connection with the experiment on oxygen isotope effect of Bi2Sr2CaCu2O8 with the angle-resolved photoemission spectroscopy (ARPES), we theoretically study the isotope-induced band shift in ARPES by the Hartree–Fork and quantum Monte Carlo methods. We find that this band shift can be clarified based on a quadratically coupled electron–phonon (e–ph) model. The large ratio of band shift versus phonon energy change is connected with the softening effect of phonon, and the positive–negative sign change is due to the momentum dependence of the e–ph coupling.