The effect of disorder in high-$T_{\mathrm{c}}$ superconductors is investigated from the viewpoint of photoinduced quasiparticle (QP) dynamics, obtained through time-resolved pump-probe spectroscopy. We perform the measurements on an optimally doped (OPD) ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) with an out-of-plane disorder induced by Bi-Sr substitution $\left(x\right)$, which is present in standard Bi2212 but is not usually controlled. Based on the systematic change of the disorder with controlled $x$, we identify the changes in the dynamics of QP relaxation and gap formation in superconducting (SC) and pseudogap (PG) states. The onset temperature $T^{*}$ of the PG response increases with an increase in $x$, which is more significant than the slight decrease in $T_{\mathrm{c}}$. These properties are equivalently reflected in the destruction fluences of the SC and PG states. Bi-Sr substitution also accelerates relaxation times for SC and PG QPs, which can be due to the increased phonon scattering probability caused by the disorder. In contrast, the SC gap recovery observed in the strongly excited condition shows an identical fluence dependence for various $x$, implying that the disorder does not significantly contribute to coherent gap formation.

• Received 8 June 2021
• Revised 5 August 2021
• Accepted 26 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.094507