We report a fine tuned doping study of strongly overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate $${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta}$$Bi 2 Sr 2 CaCu 2 O 8 + δ , we report the observation of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase. While our data hint at the possible presence of an incipient nematic quantum critical point, the doping dependence of the nematic fluctuations deviates significantly from a canonical quantum critical scenario. The observed nematic instability rather appears to be tied to the presence of a van Hove singularity in the band structure.

Although more than 20 years have passed, the identification of the superconducting order parameter in cuprates is still under debate. Here, we show that the gap size near the nodes is a good candidate for the order parameter: it scales with the critical temperature $T_c$ over a wide doping range and displays a significant temperature dependence below $T_c$ in both the underdoped and the overdoped regimes. In contrast, the gap size at the antinodes does not scale with $T_c$ in the underdoped regime and appears to be controlled by the pseudogap which persists below $T_c$.

We report Raman measurements on ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ single crystals that allow us to quantitatively evaluate the doping dependence of the density of Cooper pairs in the superconducting state. We show that the drastic loss of Cooper pairs in the antinodal region as the doping level is reduced is concomitant with a deep alteration of the quasiparticles dynamic above $T_c$ and consistent with a pseudogap that competes with superconductivity. Our data also reveal that the overall density of Cooper pairs evolves with doping, distinctly from the superfluid density above the doping level $p_c=0.2$.

The mechanism of unconventional superconductivity is still unknown despite over 25 years passing since the discovery of high-T(c) cuprate superconductors by Bednorz and Muller (1986 Z. Phys. B 64 189). Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole-doped curates, namely, how superconductivity and the critical temperature T(c) are affected by the pseudogap.