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.

High-transition-temperature (high-T(c)) superconductivity develops near antiferromagnetic phases, and it is possible that magnetic excitations contribute to the superconducting pairing mechanism. To assess the role of antiferromagnetism, it is essential to understand the doping and temperature dependence of the two-dimensional antiferromagnetic spin correlations. The phase diagram is asymmetric with respect to electron and hole doping, and for the comparatively less-studied electron-doped materials, the antiferromagnetic phase extends much further with doping and appears to overlap with the superconducting phase. The archetypal electron-doped compound Nd2-xCexCuO4+/-delta (NCCO) shows bulk superconductivity above x approximately 0.13 (refs 3, 4), while evidence for antiferromagnetic order has been found up to x approximately 0.17 (refs 2, 5, 6). Here we report inelastic magnetic neutron-scattering measurements that point to the distinct possibility that genuine long-range antiferromagnetism and superconductivity do not coexist. The data reveal a magnetic quantum critical point where superconductivity first appears, consistent with an exotic quantum phase transition between the two phases. We also demonstrate that the pseudogap phenomenon in the electron-doped materials, which is associated with pronounced charge anomalies, arises from a build-up of spin correlations, in agreement with recent theoretical proposals.