Spontaneous breaking of mirror symmetry in a cuprate beyond critical doping

Identifying ordered phases and their underlying symmetries in materials that exhibit high-temperature superconductivity is an important step towards understanding the mechanism of that phenomenon. Indeed, the critical behaviour related to phase transitions of those ordered phases is expected to be correlated with the superconductivity. In cuprate materials, efforts to find such ordered phases have mainly focused on symmetry breaking in the pseudogap region whereas the Fermi-liquid-like metallic region beyond the so-called critical doping at which the pseudogap disappears has been regarded as a trivial disordered state. Here, we uncover a broken mirror symmetry in the Fermi-liquid-like phase in (Bi,Pb) 2 Sr 2 CaCu 2 O 8+ δ beyond the critical doping. We do this by tracking the temperature dependence of the rotational-anisotropy of second-harmonic generation for two different dopings. We observe behaviour reminiscent of an order parameter with an onset temperature that coincides with the strange metal to Fermi-liquid-like metal crossover. Angle-resolved photoemission spectroscopy shows that the quasiparticle coherence between CuO 2 bilayers is enhanced in proportion to the symmetry-breaking response as a function of temperature, suggesting that the change in metallicity and symmetry breaking are linked. These observations contradict the conventional quantum disordered scenario for over-critical-doped cuprates. The Fermi liquid state in highly doped superconducting cuprates is normally thought of as disordered. Now, an observation of broken mirror symmetry in that phase suggests otherwise.