Coupling to a phononic mode in $Bi_{2-x}Pb_xSr_2CaCu_2O_{8+\delta}$: Angle-resolved photoemission

The kink in the dispersion and the drop in the width observed by angle-resolved photoemission in the nodal direction of the Brillouin zone of $\mathrm{Bi_{2-x}Pb_xSr_2CaCu_2O_{8+ \delta}}$ (abbreviated as (Pb)Bi2212) has attracted broad interest [1-3]. Surprisingly optimally lead-doped (Pb)Bi2212 with $\mathrm{T_C>89K}$ as well as the shadow band were not investigated so far, although the origin of the kink and the drop is still under strong debate. In this context a resonant magnetic-mode scenario and an electron-phonon coupling scenario are discussed controversially. Here we analyze the relevant differences between both scenarios and conclude that the kink and the drop are caused by a coupling of the electronic system to a phononic mode at least in the nodal direction. It is found that besides the dispersion and the drop in the width also the peak height as a new criterion can be used to define the energy scale of the interaction, giving a new means for a precise and consistent determination of the kink energy.