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Lattice contribution to the electronic self-energy in complex correlatedoxides is a fascinating subject that has lately stimulated lively discussions.Expectations of electron-phonon self-energy effects for simpler materials, suchas Pd and Al, have resulted in several misconceptions in strongly correlatedoxides. Here we analyze a number of arguments claiming that phonons cannot bethe origin of certain self-energy effects seen in high-$T_c$ cupratesuperconductors via angle resolved photoemission experiments (ARPES), includingthe temperature dependence, doping dependence of the renormalization effects,the inter-band scattering in the bilayer systems, and impurity substitution. Weshow that in light of experimental evidences and detailed simulations, thesearguments are not well founded.

Aspects of Electron-Phonon Self-Energy Revealed from Angle-Resolved Photoemission Spectroscopy