The cuprate high temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature T CDW and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases [1,2]. To address this issue it is important to extract the energy scale ∆ CDW associated with the charge modulations, and to compare it with the pseudogap (PG) ∆ PG and the superconducting gap ∆ SC . However, while T CDW is well-characterized from earlier works [3] little has been known about ∆ CDW until now. Here, we report the extraction of ∆ CDW for several cuprates using electronic Raman spectroscopy.Crucially, we find that, upon approaching the parent Mott state by lowering p, ∆ CDW increases in a manner similar to the doping dependence of ∆ PG and ∆ SC . This shows that CDW is an unconventional order, and that the above three phases are controlled by the same electronic correlations. In addition, we find that ∆ CDW ≈ ∆ SC over a substantial doping range, which is suggestive of an approximate emergent symmetry connecting the charge modulated phase with superconductivity [4][5][6][7][8][9].In recent years, many experiments and different techniques have established the ubiquity of CDW order in cuprates [3]. In particular, these works have determined T CDW (p), which displays a dome-like shape on the temperature-doping (T − p) phase diagram, in a fashion reminiscent of the superconducting dome T SC (p), even though the former order is present over a much narrower p-range, and mostly below optimal doping. The CDW is found to compete with superconductivity [10-16] but there are indications that the interplay between the two phenomena might be more complex than a simple competition [17,18].The energy scale ∆ CDW associated with the CDW has attracted far less experimental attention, even though this quantity is crucial to address several important ques-tions such as the following. (a) First, whether the CDW is a conventional order i.e., a phase whose existence can be understood within a scenario of weakly interacting electrons. A tell-tale signature of it would be if T CDW (p) ∝ ∆ CDW (p). On the other hand if their doping trends are different, as is famously the case of the superconducting order, it implies unconventional order, which is a consequence of strongly interacting electrons.Here we show that this is also the case of the CDW and, therefore, it is an unconventional order. (b) Second, a comparison of the magnitudes and the doping dependencies of ∆ CDW (p), ∆ SC (p) and ∆ PG (p) is important to understand the relation between these three phenomena. We show that these three energy scales have rather similar doping evolutions, implying that it is likely that they have a common origin in terms of a driving electronic interaction. Moreover, we find that the magnitude of ∆ CDW (p) and of ∆ SC (p) are comparable over a significant doping range, which is consistent with a concept that has ...

Combining electronic Raman scattering experiments with cellular dynamical mean field theory, we present evidence of the pseudogap in the superconducting state of various hole-doped cuprates. In Bi2Sr2CaCu2O 8+δ we track the superconducting pseudogap hallmark, a peak-dip feature, as a function of temperature T and doping p, well beyond the optimal one. We show that, at all temperatures under the superconducting dome, the pseudogap disappears at the doping pc, between 0.222 and 0.226, where also the normal-state pseudogap collapses at a Lifshitz transition. This demonstrates that the superconducting pseudogap boundary forms a vertical line in the T − p phase diagram.Discovered thirty years ago [1], the copper oxide (cuprate) superconductors have not ceased to arise interest because their critical temperature T c is incredibly high at ambient pressure in comparison with conventional superconductors. Central to the high-T c cuprate problem is the challenge to understand the pseudogap (PG) state. In the normal phase, where the PG has been studied extensively, it manifests below a characteristic temperature T * > T c as a loss of low energy spectral weight in spectroscopic responses [2][3][4][5][6][7][8][9][10][11][12][13][14][15], and indirectly in thermodynamical and transport properties [16][17][18][19]. Its properties cannot be accounted for by the standard Fermi liquid theory of metals [20,21].An even greater challenge is to establish whether the PG exists in the superconducting phase, and if yes, what its doping dependence is. This is crucial to understand the relation between superconductivity and the pseudogap [22][23][24][25][26], which remains far from being wellunderstood [27,28]. However, there are only very few probes that can disentangle a pseudogap from a superconducting gap. Note, even when the doping end-point of the normal state PG is known, it is unclear how that extrapolates in the superconducting phase, since it involves crossing a phase boundary. In the absence of an explicit method to identify the PG in the superconducting phase, this can be settled only through normal state extrapolations that require involved data analysis of heat capacity [16] and angle-resolved photo-emission spectra (ARPES) [14], or of magneto-resistivity and nuclear magnetic resonance measurements [18,[29][30][31][32] under application of very high magnetic fields.In this article, we present evidence that the PG develops in the SC state of different under-doped compounds, showing that it is a universal property of cuprates. In the case of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212), we are able to follow the PG evolution with doping under the superconducting dome. We show that the pseudogap end is a vertical line in the T −p phase diagram within a narrow range of doping 0.222 < p c < 0.226 [33], the doping level where a Lifshitz transition from a hole-like to an electron-like Fermi surface takes place in the underlying electronic structure [13,34]. Our experimental findings are analyzed within the cellular dynamical mean-field theory ...