The pseudogap region of the phase diagram is an important unsolved puzzle in the field of high-transition-temperature (high-T(c)) superconductivity, characterized by anomalous physical properties. There are open questions about the number of distinct phases and the possible presence of a quantum-critical point underneath the superconducting dome. The picture has remained unclear because there has not been conclusive evidence for a new type of order. Neutron scattering measurements for YBa(2)Cu(3)O(6+delta) (YBCO) resulted in contradictory claims of no and weak magnetic order, and the interpretation of muon spin relaxation measurements on YBCO and of circularly polarized photoemission experiments on Bi(2)Sr(2)CaCu(2)O(8+delta)(refs 12, 13) has been controversial. Here we use polarized neutron diffraction to demonstrate for the model superconductor HgBa(2)CuO(4+delta) (Hg1201) that the characteristic temperature T* marks the onset of an unusual magnetic order. Together with recent results for YBCO, this observation constitutes a demonstration of the universal existence of such a state. The findings appear to rule out theories that regard T* as a crossover temperature rather than a phase transition temperature. Instead, they are consistent with a variant of previously proposed charge-current-loop order that involves apical oxygen orbitals, and with the notion that many of the unusual properties arise from the presence of a quantum-critical point.

Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

Since the discovery of superconductivity at elevated temperatures in the copper oxide materials there has been a considerable effort to find universal trends and correlations amongst physical quantities, as a clue to the origin of the superconductivity. One of the earliest patterns that emerged was the linear scaling of the superfluid density (rho(s)) with the superconducting transition temperature (T(c)), which marks the onset of phase coherence. This is referred to as the Uemura relation, and it works reasonably well for the underdoped materials. It does not, however, describe optimally doped (where T(c) is a maximum) or overdoped materials. Similarly, an attempt to scale the superfluid density with the d.c. conductivity (sigma(dc)) was only partially successful. Here we report a simple scaling relation (rho(s) proportional, variant sigma(dc)T(c), with sigma(dc) measured at approximately T(c)) that holds for all tested high-T(c) materials. It holds regardless of doping level, nature of dopant (electrons versus holes), crystal structure and type of disorder, and direction (parallel or perpendicular to the copper-oxygen planes).

Upon introducing charge carriers into the copper-oxygen sheets of the enigmatic lamellar cuprates, the ground state evolves from an insulator to a superconductor and eventually to a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (ρ ∝ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here, we first demonstrate for the quintessential compound HgBa 2 CuO 4+δ a dramatic switch from linear to purely quadratic (Fermi liquid-like, ρ ∝ T 2 ) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives insight into the p-T phase diagram and reveals the fundamental resistance per copper-oxygen sheet in both linear (ρ ☐ = A 1☐ T) and quadratic (ρ ☐ = A 2☐ T 2 ) regimes, with A 1☐ ∝ A 2☐ ∝ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insight into the nonuniversal features exhibited by certain compounds.

Cuprate high-T c superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest T c s) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasiparticle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (h ω) 2 + (pπk B T) 2 . Magnetotransport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T 2 dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω-and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.optical spectroscopy | superconductivity | mass renormalization | self energy T he compound HgBa 2 CuO 4+δ (Hg1201) is the single-layer cuprate that exhibits the highest T c (97 K). We therefore measured the optical conductivity of strongly underdoped single crystals of Hg1201 ðT c = 67 KÞ. Here we are interested in the optical conductivity of the CuO 2 layers. We therefore express the optical conductivity as a 2D sheet conductance GðωÞ = d c σðωÞ, where d c is the interlayer spacing. The real part of the sheet conductance normalized by the conduction quantum G 0 = 2e 2 =h is shown in Fig. 1. As seen in the figure, a gap-like suppression below 140 meV is clearly observable for temperatures below T c and remains visible in the normal state up to ∼250 K. This is a clear optical signature of the pseudogap. We also observe the zero-energy mode due to the free charge carrier response, which progressively narrows upon lowering the temperature. In materials where the charge carrier relaxation is dominated by impurity scattering, the width of this "Drude" peak corresponds to the relaxation rate of the charge carriers. Relaxation processes arising from interactions have the effect of replacing the constant (frequency-independent) relaxation rate with a frequencydependent one. The general expression for the optical conductivity of interacting electrons is then Gðω; TÞ = iπK Zω + Mðω; TÞ G 0 :[1]The spectral weight K corresponds to minus the kinetic energy if the frequency integration of the experimental data is restricted to intraband transitions. The effect of electron-electron interactions and coupling to collective mo...

The metallic state of the underdoped high-Tc cuprates has remained an enigma: How may seemingly disconnected Fermi surface segments, observed in zero magnetic field as a result of the opening of a partial gap (the pseudogap), possess conventional quasiparticle properties? How do the small Fermi-surface pockets evidenced by the observation of quantum oscillations (QO) emerge as superconductivity is suppressed in high magnetic fields? Such QO, discovered in underdoped YBa2Cu3O6.5 (Y123) and YBa2Cu4O8 (Y124), signify the existence of a conventional Fermi surface (FS). However, due to the complexity of the crystal structures of Y123 and Y124 (CuO2 double-layers, CuO chains, low structural symmetry), it has remained unclear if the QO are specific to this particular family of cuprates. Numerous theoretical proposals have been put forward to explain the route toward QO, including materials-specific scenarios involving CuO chains and scenarios involving the quintessential CuO2 planes. Here we report the observation of QO in underdoped HgBa2CuO4+{\delta} (Hg1201), a model cuprate superconductor with individual CuO2 layers, high tetragonal symmetry, and no CuO chains. This observation proves that QO are a universal property of the underdoped CuO2 planes, and it opens the door to quantitative future studies of the metallic state and of the Fermi-surface reconstruction phenomenon in this structurally simplest cuprate.Comment: 17 pages, 5 figure

Charge-density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the CuO 2 planes, such as orthorhombic YBa 2 Cu 3 O y (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal HgBa 2 CuO 4þ (Hg1201). We have measured the Hall (R H ), Seebeck (S), and Nernst () coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field R H ðTÞ and SðTÞ are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative R H and S are signatures of a small electron pocket caused by Fermi-surface reconstruction, attributed to charge-density-wave modulations observed in the same range of doping and temperature. We deduce that a similar Fermi-surface reconstruction takes place in Hg1201, evidence that density-wave order exists in this material. A striking similarity is also found in the normal-state Nernst coefficient ðTÞ, further supporting this interpretation. Given the model nature of Hg1201, Fermi-surface reconstruction appears to be common to all hole-doped cuprates, suggesting that density-wave order is a fundamental property of these materials. There is a growing body of evidence that competing ordered states shape the phase diagram of the cuprates, and the identification of those states is currently a central challenge of high-temperature superconductivity. In the La 2 CuO 4 -based cuprates, whose maximal T c does not exceed 40 K, the existence of unidirectional densitywave order involving spin and charge modulations, known as stripe order [1,2] [9,10], a material with a maximal T c of 93 K, shows that its Fermi surface also undergoes a reconstruction [11,12]. Comparative measurements of the Seebeck coefficient in YBCO and Eu-LSCO reveal a detailed similarity [7,8], suggesting that Fermi-surface reconstruction (FSR) in YBCO is caused by some form of stripe order.Charge-density-wave modulations were recently detected in YBCO, via high-field nuclear magnetic resonance (NMR) [13] and x-ray-scattering [14][15][16][17][18] measurements, in the range of temperature and doping where FSR occurs [8,19]. Although the detailed structure of these modulations remains to be clarified, there is little doubt that they are responsible for the FSR in YBCO.The fundamental question, then, is whether such charge modulations are a generic property of the cuprates. Because both the low-temperature tetragonal structure of Eu-LSCO and the orthorhombic structure of YBCO distort the square CuO 2 planes and impose a preferred direction, charge modulations are perhaps triggered or stabilized by these particular forms of unidirectional distortion. To answer that question, we need to examine a cuprate material with square CuO 2 planes. For that purpose, the model material is HgBa 2 CuO 4þ (Hg1201), a tetragonal cuprate with the highest maximal T c of all single-layer cuprates (97 K) [20,21], in which no charge or spin modulations have yet been reported. ...

(2008)], this establishes the universal existence of a genuine novel magnetic phase in underdoped cuprates with high maximal Tc (above 90 K at optimal doping). Here we report a systematic study of an underdoped Hg1201 sample (Tc = 75 K), the result of which is consistent with the previously established doping dependence of the magnetic signal. We present an assumption-free analysis of all the data available for Hg1201. Depending on how the hole concentration is estimated, comparison with the results for YBCO leads to different competition scenarios between the q = 0 magnetic order and the spin-density-wave order found in heavily underdoped YBCO.