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The 40-70 meV band-structure renormalization (so-called kink) inhigh-temperature cuprate superconductors - which has been mainly interpreted interms of electron-boson coupling - is observed to be strongly suppressed bothabove the superconducting transition temperature and under optical excitation.We employ equilibrium and time- and angle-resolved photoemission spectroscopy,in combination with Migdal-Eliashberg simulations, to investigate thesuppression of the near-nodal kink in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Weshow that the $\sim$30$\%$ decrease of the kink strength across thesuperconducting-to-normal-state phase transition can be entirely accounted forby the filling of the superconducting gap, without additional consideration oftemperature-dependent electron-boson coupling. Our findings demonstrate thatconsideration of changes in the density of states is essential toquantitatively account for the band structure renormalization effects incuprates.

Kink in cuprates: the role of the low-energy density of states