Theoretical study on isotopic shift in angle-resolved photoemission spectra of Bi2Sr2CaCu2O8

We develop a path-integral theory to study the angle-resolved photoemission spectra (ARPES) of high-T_c superconductors based on a two-dimensional model for the CuO2 conduction plane, including both electron-electron (e-e) and electron-phonon (e-ph) interactions. Comparing our result with the experimental one of Bi2Sr2CaCu2O8, we find that the experimentally observed isotopic band shift in ARPES is due to the off-diagonal quadratic e-ph coupling, whereas the presence of e-e repulsion partially suppresses this effect.