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 ${\text{Bi}}_{2-x}{\text{Pb}}_x{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ [(Pb)Bi2212] has attracted broad interest. Surprisingly, optimally lead-doped (Pb)Bi2212 with $T_C>89\text{K}$ and the shadow band have not been 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 have been 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 previously employed criterion can be used to define the energy scale of the interaction, giving a previously unknown means for a precise and consistent determination of the kink energy.

• Received 8 January 2007

DOI:https://doi.org/10.1103/PhysRevB.77.054520