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Identifying ordered phases and their underlying symmetries is the first andmost important step toward understanding the mechanism of high-temperaturesuperconductivity; critical behaviors of ordered phases are expected to becorrelated with superconductivity. Efforts to find such ordered phases havebeen focused on symmetry breaking in the pseudogap region while the Fermiliquid-like metal region beyond the so-called critical doping $p_{c}$ has beenregarded as a trivial disordered state. Here, we used rotational anisotropysecond harmonic generation and uncovered a broken mirror symmetry in the Fermiliquid-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-breakingresponse, we verify an order parameter-like behavior with the onset temperature$T_{up}$ at which the strange metal to Fermi liquid-like-metal crossover takesplace. Complementary angle-resolved photoemission study showed that thequasiparticle coherence between $\mathrm{CuO_{2}}$ bilayers is enhanced inproportion 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 forover-critical-doped cuprates and provide new insight into the nature of thequantum critical point in cuprates.

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