The temperature dependent evolution of the renormalization effect in optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_{0.92}{\mathrm{Y}}_{0.08}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ along the nodal direction has been studied via angle-resolved photoemission spectroscopy. Fine structure is observed in the real part of the self-energy $\left(\mathrm{Re}\Sigma \right)$, including a subkink and maximum, suggesting that electrons couple to a spectrum of bosonic modes, instead of just one mode. Upon cooling through the superconducting phase transition, the fine structures of the extracted $\mathrm{Re}\Sigma$ exhibit a two-processes evolution demonstrating an interplay between kink renormalization and superconductivity. We show that this two-process evolution can be qualitatively explained by a simple Holstein model in which a spectrum of bosonic modes is considered.

• Received 29 February 2008

DOI:https://doi.org/10.1103/PhysRevB.77.140504