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