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 ...

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 , 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.

We study the temperature-dependent electronic B1g Raman response of a slightly under-doped single crystal HgBa2Ca2Cu3O 8+δ with a superconducting critical temperature Tc =122 K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at Tc . This result hints at an unconventional pairing mechanism, whereas spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to reproduce all the main features of the B1g Raman response and explain the peak-dip behavior in terms of a nontrivial relationship between the superconducting and the pseudo gaps.PACS numbers: 74.72. Gh,74.25.nd,74.20.Mn,74.72.Kf Conventional superconductors are well understood within the Bardeen-Cooper-Schrieffer (BCS) theory [1]: below a critical transition temperature T c , electrons at a characteristic energy (the Fermi energy) bind into Cooper pairs by an effective attractive interaction mediated by lattice vibrations (phonons) [2]. The Bose condensate of pairs displays then zero resistance to electrical conduction and a gap opens in spectroscopic observables by a transfer of spectral weight from the Fermi level to higher energies. The BCS pairing mechanism, however, has not been able to account for the high T c observed in copperoxide (cuprate) superconductors. In these materials the isotopic effect is extremely weak and does not suggest a strongly coupled phonon-mediated superconductivity [3].The nature of the pairing interaction has therefore remained controversial. Possible proposals include strong electronic correlations stemming from Mott physics [4] or the competition with other exotic phases such as charge [5][6][7], spin density [8-10] waves or loop currents [11].The scenario is further complicated by the presence of another gap (the pseudogap), which is an ingredient missing in the BCS description. The pseudogap manifests itself above T c as a loss of quasiparticle spectral weight [12][13][14]. Whether or not the pseudogap plays any role in the high-T c mechanism, this remains a fundamental open question. This inherent complexity of the cuprates has hidden key features of the pairing mechanism in most experiments, preventing a satisfactory understanding of high T c superconductivity.In this article we present an electronic Raman scattering study in the B 1g geometry on a slightlyunderdoped (UD) three-copper-oxide-layer compound HgBa 2 Ca 2 Cu 3 O 8+δ (Hg-1223). We reveal a nontrivial relationship between the pair-breaking peak (PP), which corresponds to two Bogoliubov quasiparticle excitations, and a loss of spectral weight (dip) appearing on its higher-energy side. Remarkably, the PP and dip disappear simultaneously at T c , indicating a transfer of spectral weight from the dip electronic states to the PP at lower energies. This behavior is in sharp contrast with the BCS pairing mechanism, which involves only the lo...

Cubic SrTiO3 becomes tetragonal below 105 K. The antiferrodistortive (AFD) distortion leads to clockwise and counter-clockwise rotation of adjacent TiO6 octahedra. This insulator becomes a metal upon the introduction of extremely low concentration of n-type dopants. However, signatures of the structural phase transition in charge conduction have remained elusive. Employing the Montgomery technique, we succeed in resolving the anisotropy of charge conductivity induced by the AFD transition, in the presence of different types of dopants. We find that the slight lattice distortion (< 6 × 10 −4 ) gives rise to a twenty percent anisotropy in charge conductivity, in agreement with the expectations of band calculations. Application of uniaxial strain amplifies the detectable anisotropy by disfavoring one of the three possible tetragonal domains. In contrast with all other known anisotropic Fermi liquids, the anisotropy has opposite signs for elastic and inelastic scattering. Increasing the concentration of dopants leads to a drastic shift in the temperature of the AFD transition either upward or downward. The latter result puts strong constraints on any hypothetical role played by the AFD soft mode in the formation of Cooper pairs and the emergence of superconductivity in SrTiO3.

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We report an original procedure for the elaboration of very high-quality single crystals of superconducting HgBaCaCuO mercury cuprates. These single crystals are unique, with very high-quality surface paving the way for spectroscopic, transport, and thermodynamic probes in order to understand the hole-doped cuprate phase diagram. Annealing allows one to optimize T up to T = 133 K. The superconductivity transition width of about 2 K indicates that they are homogeneous. We show for the first time that, with adequate heat treatment, Hg-1223 can be largely underdoped and its doping level controlled. Importantly, the crystal structure was studied in detail by single-crystal X-ray diffraction, and we have identified the signature of the underdoping by a detailed sample characterization and micro-Raman spectroscopy measurements.