Critical photoinduced reflectivity relaxation dynamics in single-layer Bi-based cuprates near the pseudogap end point

A comprehensive study of photoinduced transient reflectivity dynamics in heavily overdoped single-layer cuprate (Bi,Pb)$_{2}$Sr$_{2}$CuO$_{6+\delta}$ (Pb-Bi2201), across the end points of the pseudogap and superconducting phases, has been conducted using optical ultrafast time-resolved pump-probe spectroscopy. In the Pb-Bi2201 just before reaching the pseudogap end point, the transient reflectivity dynamics above $T_{{\rm c}}$ resemble the pseudogap response observed in optimally doped La-Bi2201. At low temperatures, however, the relaxation time exhibits a power-law divergence, $\tau\sim10\hbar/k_{\mathrm{B}}T$, signaling quantum critical behavior at the pseudogap end point doping. A similar power-law increase in relaxation time is also observed in Pb-Bi2201 just beyond the pseudogap doping end point, though it is less pronounced.