Spontaneous breaking of mirror symmetry beyond critical doping in Pb-Bi2212

Identifying ordered phases and their underlying symmetries is the first and most important step toward understanding the mechanism of high-temperature superconductivity; critical behaviors of ordered phases are expected to be correlated with superconductivity. Efforts to find such ordered phases have been focused on symmetry breaking in the pseudogap region while the Fermi liquid-like metal region beyond the so-called critical doping $p_{c}$ has been regarded as a trivial disordered state. Here, we used rotational anisotropy second harmonic generation and uncovered a broken mirror symmetry in the Fermi liquid-like phase in (Bi,Pb)$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ with $p = 0.205 > p_{c}$. By tracking the temperature evolution of the symmetry-breaking response, we verify an order parameter-like behavior with the onset temperature $T_{up}$ at which the strange metal to Fermi liquid-like-metal crossover takes place. Complementary angle-resolved photoemission study showed that the quasiparticle coherence between $\mathrm{CuO_{2}}$ bilayers is enhanced in proportion to the symmetry-breaking response as a function of temperature, indicating that the change in metallicity and symmetry breaking are linked. These observations contradict the conventional quantum disordered scenario for over-critical-doped cuprates and provide new insight into the nature of the quantum critical point in cuprates.