Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature

Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking

The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.

Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates

The cuprate high-temperature superconductors have been the focus of unprecedentedly intense and sustained study not only because of their high superconducting transition temperatures, but also because they represent the most exquisitely investigated examples of highly correlated electronic materials. In particular, the pseudogap regime of the phase diagram exhibits a variety of mysterious emergent behaviors. In the last few years, evidence from NMR and scanning tunneling microscopy (STM) studies, as well as from a new generation of X-ray scattering experiments, has accumulated, indicating that a general tendency to short-range-correlated incommensurate charge density wave (CDW) order is "intertwined" with the superconductivity in this regime. Additionally, transport, STM, neutron-scattering, and optical experiments have produced evidence--not yet entirely understood--of the existence of an associated pattern of long-range-ordered point-group symmetry breaking with an electron-nematic character. We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. Although the possibilities of a sharp phase transition and long-range CDW order are precluded in such systems, we show that any discrete symmetry-breaking aspect of the charge order--nematicity in the case of the unidirectional (stripe) CDW we consider explicitly--generically survives up to a nonzero critical disorder strength. Such "vestigial order," which is subject to unambiguous macroscopic detection, can serve as an avatar of what would be CDW order in the ideal, zero disorder limit. Various recent experiments in the pseudogap regime of the hole-doped cuprates are readily interpreted in light of these results.

Optical birefringence and dichroism of cuprate superconductors in the THz regime

The presence of optical polarization anisotropies, such as Faraday or Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter. The recent discovery of a Kerr effect using near-IR light in the pseudogap phase of the cuprates can be regarded as a strong evidence for a spontaneous symmetry breaking and the existence of an anomalous long-range ordered state. In this work we present a high precision study of the polarimetry properties of the cuprates in the THz regime. While no Faraday effect was found in this frequency range to the limits of our experimental uncertainty (1.3 milli-radian or 0.07°), a small but significant polarization rotation was detected that derives from an anomalous linear dichroism. In YBa2Cu3Oy the effect has a temperature onset that mirrors the pseudogap temperature T* and is enhanced in magnitude in underdoped samples. In x=1/8 La2-xBaxCuO4, the effect onsets above room temperature, but shows a dramatic enhancement near a temperature scale known to be associated with spin- and charge-ordered states. These features are consistent with a loss of both C4 rotation and mirror symmetry in the electronic structure of the CuO2 planes in the pseudogap state.

Cu(Ir₁ - xCrx)₂S₄: a model system for studying nanoscale phase coexistence at the metal-insulator transition

Increasingly, nanoscale phase coexistence and hidden broken symmetry states are being found in the vicinity of metal-insulator transitions (MIT), for example, in high temperature superconductors, heavy fermion and colossal magnetoresistive materials, but their importance and possible role in the MIT and related emergent behaviors is not understood. Despite their ubiquity, they are hard to study because they produce weak diffuse signals in most measurements. Here we propose Cu(Ir_{1 − x}Cr_x)₂S₄ as a model system, where robust local structural signals lead to key new insights. We demonstrate a hitherto unobserved coexistence of an Ir⁴⁺ charge-localized dimer phase and Cr-ferromagnetism. The resulting phase diagram that takes into account the short range dimer order is highly reminiscent of a generic MIT phase diagram similar to the cuprates. We suggest that the presence of quenched strain from dopant ions acts as an arbiter deciding between the competing ground states.

Evidence of chiral order in the charge-ordered phase of superconducting La1.875Ba0.125Cuo4 single crystals using polar Kerr-effect measurements

High resolution polar Kerr effect measurements were performed on La1.875Ba0.125CuO4 single crystals revealing that a finite Kerr signal is measured below an onset temperature TK that coincides with the charge ordering transition temperature TCO. We further show that the sign of the Kerr signal cannot be trained with the magnetic field, is found to be the same on opposite sides of the same crystal, and is odd with respect to strain in the diagonal direction of the unit cell. These observations are consistent with a chiral "gyrotropic" order above Tc for La1.875Ba0.125CuO4; similarities to other cuprates suggest that it is a universal property in the pseudogap regime.

Superconducting pairing and the pseudogap in the nematic dynamical stripe phase of La2-xSrxCuO4

Fully absorption coefficient corrected Raman spectra were obtained in La2-xSrxCuO4. The B1g spectra have a Fleury-Loudon type two-magnon peak (resonant term) whose energy decreases from 3180 cm(-1) (394 meV) to 440 cm(-1) (55 meV) on increasing the carrier density from x = 0 to 0.25, while the B2g spectra have a 1000-3500 cm(-1) (124-434 meV) hump (hill) whose lower-edge energy increases from x = 0 to 0.115 and then stays constant to x = 0.25. The B2g hump is assigned to the electronic scattering (non-resonant term) of the spectral function with magnetic self-energy. The completely different carrier density dependence arises from anisotropic magnetic excitations of spin-charge stripes. The B1g spectra were assigned to the sum of k ∥  and k⊥ stripe excitations and the B2g spectra to k⊥ stripe excitations according to the calculation by Seibold and Lorenzana (2006 Phys. Rev. B 73 144515). The k ∥  and k⊥ stripe excitations in fluctuating spin-charge stripes were separately detected for the first time. The appearance of only k⊥ stripe excitations in the electronic scattering arises from the charge hopping perpendicular to the stripe. This is the same direction as the Burgers vector of the edge dislocation in metal. The successive charge hopping in the Burgers vector direction across the charge stripes may cause Cooper pairs as predicted by Zaanen et al (2004 Ann. Phys. 310 181). Indeed, this is supported by the experimental fact that the superconducting coherent length coincides with the inter-charge stripe distance in the wide carrier density range. The one-directional charge hopping perpendicular to the stripe causes the flat Fermi surface and the pseudogap near (π,0) and (0,π), but the states around (π/2,π/2) cannot be produced. The low-energy Raman scattering disclosed that the electronic states at the Fermi arc around (π/2,π/2) are coupled to the A1g soft phonon of the tetragonal-orthorhombic phase transition. This suggests that the Fermi arc is produced by the electron-phonon interaction. All the present Raman data suggest that Cooper pairs are formed at moving edge dislocations of dynamical charge stripes.

Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity

Unconventional superconductivity (SC) is said to occur when Cooper pair formation is dominated by repulsive electron-electron interactions, so that the symmetry of the pair wave function is other than an isotropic s-wave. The strong, on-site, repulsive electron-electron interactions that are the proximate cause of such SC are more typically drivers of commensurate magnetism. Indeed, it is the suppression of commensurate antiferromagnetism (AF) that usually allows this type of unconventional superconductivity to emerge. Importantly, however, intervening between these AF and SC phases, intertwined electronic ordered phases (IP) of an unexpected nature are frequently discovered. For this reason, it has been extremely difficult to distinguish the microscopic essence of the correlated superconductivity from the often spectacular phenomenology of the IPs. Here we introduce a model conceptual framework within which to understand the relationship between AF electron-electron interactions, IPs, and correlated SC. We demonstrate its effectiveness in simultaneously explaining the consequences of AF interactions for the copper-based, iron-based, and heavy-fermion superconductors, as well as for their quite distinct IPs.

The k-space origins of scattering in Bi2Sr2CaCu2O8+x

We demonstrate a general, computer automated procedure that inverts the reciprocal space scattering data (q-space) that are measured by spectroscopic imaging scanning tunnelling microscopy (SI-STM) in order to determine the momentum space (k-space) scattering structure. This allows a detailed examination of the k-space origins of the quasiparticle interference (QPI) pattern in Bi2Sr2CaCu2O8+x within the theoretical constraints of the joint density of states (JDOS). Our new method allows measurement of the differences between the positive and negative energy dispersions, the gap structure and an energy dependent scattering length scale. Furthermore, it resolves the transition between the dispersive QPI and the checkerboard ([Formula: see text] excitation). We have measured the k-space scattering structure over a wide range of doping (p ∼ 0.22-0.08), including regions where the octet model is not applicable. Our technique allows the complete mapping of the k-space scattering origins of the spatial excitations in Bi2Sr2CaCu2O8+x, which allows for better comparisons between SI-STM and other experimental probes of the band structure. By applying our new technique to such a heavily studied compound, we can validate our new general approach for determining the k-space scattering origins from SI-STM data.

Proposed chiral texture of the magnetic moments of unit-cell loop currents in the pseudogap phase of cuprate superconductors

We propose a novel chiral order parameter to explain the unusual polar Kerr effect in underdoped cuprates. It is based on the loop-current model by Varma, which is characterized by the in-plane anapole moment N and exhibits the magnetoelectric effect. We propose a helical structure where the vector N(n) in the layer n is twisted by the angle π/2 relative to N(n-1), thus breaking inversion symmetry. We show that coupling between magnetoelectric terms in the neighboring layers for this structure produces optical gyrotropy, which results in circular dichroism and the polar Kerr effect.

Surface-enhanced charge-density-wave instability in underdoped Bi2Sr(2-x)La(x)CuO(6+δ)

Neutron and X-ray scattering experiments have provided mounting evidence for spin and charge ordering phenomena in underdoped cuprates. These range from early work on stripe correlations in Nd-LSCO to the latest discovery of charge-density-waves in YBa2Cu3O(6+x). Both phenomena are characterized by a pronounced dependence on doping, temperature and an externally applied magnetic field. Here, we show that these electron-lattice instabilities exhibit also a previously unrecognized bulk-surface dichotomy. Surface-sensitive electronic and structural probes uncover a temperature-dependent evolution of the CuO2 plane band dispersion and apparent Fermi pockets in underdoped Bi2 Sr(2-x) La(x) CuO(6+δ) (Bi2201), which is directly associated with an hitherto-undetected strong temperature dependence of the incommensurate superstructure periodicity below 130 K. In stark contrast, the structural modulation revealed by bulk-sensitive probes is temperature-independent. These findings point to a surface-enhanced incipient charge-density-wave instability, driven by Fermi surface nesting. This discovery is of critical importance in the interpretation of single-particle spectroscopy data, and establishes the surface of cuprates and other complex oxides as a rich playground for the study of electronically soft phases.

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ

Close to optimal doping, the copper oxide superconductors show 'strange metal' behaviour, suggestive of strong fluctuations associated with a quantum critical point. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting 'dome'. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the 'pseudogap' because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.

X-ray diffraction observations of a charge-density-wave order in superconducting ortho-II YBa2Cu3O6.54 single crystals in zero magnetic field

X-ray diffraction measurements show that the high-temperature superconductor YBa2Cu3O6.54, with ortho-II oxygen order, has charge-density-wave order in the absence of an applied magnetic field. The dominant wave vector of the charge density wave is q(CDW)=(0,0.328(2),0.5), with the in-plane component parallel to the b axis (chain direction). It has a similar incommensurability to that observed in ortho-VIII and ortho-III samples, which have different dopings and oxygen orderings. Our results for ortho-II contrast with recent high-field NMR measurements, which suggest a commensurate wave vector along the a axis. We discuss the relationship between spin and charge correlations in YBa2Cu3O(y) and recent high-field quantum oscillation, NMR, and ultrasound experiments.

Magneto-optical measurements of a cascade of transitions in superconducting La1.875Ba0.125CuO4 single crystals

Recent experiments on the original cuprate high-temperature superconductor, La(2-x)Ba(x)CuO4, revealed a remarkable sequence of phase transitions. Here we investigate such crystals with the polar Kerr effect, which is sensitive to time-reversal-symmetry breaking. Concurrent birefringence measurements accurately locate the structural phase transitions from high-temperature tetragonal to low-temperature orthorhombic, and then to lower-temperature tetragonal, at which temperature strong Kerr signal onsets. Hysteretic behavior of the Kerr signal suggests that time-reversal symmetry is already broken well above room temperature, an effect that was previously observed in high quality YBa2Cu3O(6+x) crystals.

Unusual Nernst effect suggesting time-reversal violation in the striped cuprate superconductor La(2-x)Ba(x)CuO4

The striped cuprate La(2-x)Ba(x)CuO(4) (x=1/8) undergoes several transitions below the charge-ordering temperature T(co)=54  K. From Nernst experiments, we find that, below T(co), there exists a large, anomalous Nernst signal e(N,even)(H,T) that is symmetric in field H, and remains finite as H→0. The time-reversal violating signal suggests that, below T(co), vortices of one sign are spontaneously created to relieve interlayer phase frustration.

Optical nonreciprocity in magnetic structures related to high-Tc superconductors

Rotation of the plane of polarization of reflected light (Kerr effect) is a direct manifestation of broken time-reversal symmetry and is generally associated with the appearance of a ferromagnetic moment. Here I identify magnetic structures that may arise within the unit cell of cuprate superconductors that generate polarization rotation despite the absence of a net moment. For these magnetic symmetries the Kerr effect is mediated by magnetoelectric coupling, which can arise when antiferromagnetic order breaks inversion symmetry. The structures identified are candidates for a time-reversal breaking phase in the pseudogap regime of the cuprates.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.

Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model

Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t', we find a classical critical point at temperature T(c). This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature T(c) extrapolates to zero as t' vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid-gas transition.

Mottness collapse and T-linear resistivity in cuprate superconductors

Central to the normal state of cuprate high-temperature superconductors is the collapse of the pseudo-gap, briefly reviewed here, at a critical point and the subsequent onset of the strange metal characterized by a resistivity that scales linearly with temperature. A possible clue to the resolution of this problem is the inter-relation between two facts: (i) a robust theory of T-linear resistivity resulting from quantum criticality requires an additional length scale outside the standard one-parameter scaling scenario and (ii) breaking the Landau correspondence between the Fermi gas and an interacting system with short-range repulsions requires non-fermionic degrees. We show that a low-energy theory of the Hubbard model that correctly incorporates dynamical spectral weight transfer has the extra degrees of freedom needed to describe this physics. The degrees of freedom that mix into the lower band as a result of dynamical spectral weight transfer are shown to either decouple beyond a critical doping, thereby signalling Mottness collapse, or unbind above a critical temperature, yielding strange metal behaviour characterized by T-linear resistivity.

Dichotomy in the T-linear resistivity in hole-doped cuprates

From analysis of the in-plane resistivity ρ(ab)(T) of La(2-x)Sr(x)CuO(4), we show that normal state transport in overdoped cuprates can be delineated into two regimes in which the electrical resistivity varies approximately linearly with temperature. In the low-temperature limit, the T-linear resistivity extends over a very wide doping range, in marked contrast to expectations from conventional quantum critical scenarios. The coefficient of this T-linear resistivity scales with the superconducting transition temperature T(c), implying that the interaction causing this anomalous scattering is also associated with the superconducting pairing mechanism. At high temperatures, the coefficient of the T-linear resistivity is essentially doping independent beyond a critical doping p(crit)=0.19 at which the ratio of the two coefficients is maximal. Taking our cue from earlier thermodynamic and photoemission measurements, we conclude that the opening of the normal-state pseudogap at p(crit) is driven by the loss of coherence of anti-nodal quasi-particles at low temperatures.

From a single-band metal to a high-temperature superconductor via two thermal phase transitions

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T(c)), entangled in an energy-momentum-dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

Anomalous noise in the pseudogap regime of YBa2Cu3O(7-delta)

An unusual noise component is found near and below about 250 K in the normal state of underdoped YBCO and Ca-YBCO films. This noise regime, unlike the more typical noise above 250 K, has features expected for a symmetry-breaking collective electronic state. These include large individual fluctuators, a magnetic sensitivity, and aging effects. A possible interpretation in terms of fluctuating charge nematic order is presented.

Broken rotational symmetry in the pseudogap phase of a high-T(c) superconductor

The nature of the pseudogap phase is a central problem in the effort to understand the high-transition-temperature (high-T(c)) copper oxide superconductors. A fundamental question is what symmetries are broken when the pseudogap phase sets in, which occurs when the temperature decreases below a value T*. There is evidence from measurements of both polarized neutron diffraction and the polar Kerr effect that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements and inelastic neutron scattering at low doping, and from scanning tunnelling spectroscopy at low temperature, but showed no clear relation to T*. Here we report the observation of a large in-plane anisotropy of the Nernst effect in YBa(2)Cu(3)O(y) that sets in precisely at T* throughout the doping phase diagram. We show that the CuO chains of the orthorhombic lattice are not responsible for this anisotropy, which is therefore an intrinsic property of the CuO(2) planes. We conclude that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order.

Detection of the unusual magnetic orders in the pseudogap region of a high-temperature superconducting YBa2Cu3O6.6 crystal by muon-spin relaxation

We present muon-spin relaxation (muSR) measurements on a large YBa2Cu3O6.6 single crystal in which two kinds of unusual magnetic order have been detected in the pseudogap region by neutron scattering. A comparison is made to measurements on smaller, higher quality YBa2Cu3Oy single crystals. One type of magnetic order is observed in all samples, but does not evolve significantly with hole doping. A second type of unusual magnetic order is observed only in the YBa2Cu3O6.6 single crystal. This magnetism has an ordered magnetic moment that is quantitatively consistent with the neutron experiments, but is confined to just a small volume of the sample ( approximately 3%). Our findings do not support theories that ascribe the pseudogap to a state characterized by loop-current order, but instead indicate that dilute impurity phases are the source of the unusual magnetic orders in YBa2Cu3Oy.

Circular dichroism in the angle-resolved photoemission spectrum of the high-temperature Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} superconductor: can these measurements be interpreted as evidence for time-reversal symmetry breaking?

We report first-principles computations of the angle-resolved photoemission response with circularly polarized light in Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} for the purpose of delineating contributions to the circular dichroism resulting from distortions and modulations of the crystal lattice. Comparison with available experimental results shows that the measured circular dichroism from antinodal mirror planes is reproduced in quantitative detail in calculations employing the average orthorhombic crystal structure. We thus conclude that the existing angle-resolved photoemission measurements can be understood essentially within the framework of the conventional picture, without the need to invoke unconventional mechanisms.

Pairing state with a time-reversal symmetry breaking in FeAs-based superconductors

We investigate the competition between the extended s+/--wave and dx2-y2-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole Fermi pockets, a time-reversal symmetry breaking s+id pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory and explore the experimental consequences. In such a state, spatial inhomogeneity induces a supercurrent near a nonmagnetic impurity and the corners of a square sample. The resonance mode between the s+/-- and dx2-y2-wave order parameters can be detected through the B1g Raman spectroscopy.

Spin glass behaviors compatible with a Zhang-Rice singlet within an effective model for cuprate superconductors

To address the incompatibility of Zhang-Rice singlet formation and the observed spin glass behavior, an effective model is proposed for the electronic behavior of cuprate materials. The model includes an antiferromagnetic interaction between the spin of the hole in a Zhang-Rice orbital and the spin of the hole on the corresponding copper site. While in the large interaction limit this recovers the t-J model, in the low energy limit the Zhang-Rice singlets are deformed. It is also shown that such deformation can induce random defect ferromagnetic (FM) bonds between adjacent local spins, an effect herein referred to as unusual double exchange, and then spin glass behavior shall result in the case of localized holes. A derivation of the model is also presented.

Orbital currents in extended Hubbard models of high-Tc cuprate superconductors

Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters and that they are stabilized in the thermodynamic limit if additional interactions, e.g., strong hybridization with apical oxygens, are included in the model.

Screening of point charge impurities in highly anisotropic metals: application to mu+-spin relaxation in underdoped cuprate superconductors

We calculate the screening charge density distribution due to a point charge, such as that of a positive muon (mu+), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the mu+ to nearly its value in the insulating state. The current-loop-ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This strongly suppresses the magnetic field at the mu+ site. We estimate this suppressed field in underdoped YBa2Cu3O6+x and La2-xSrxCuO4, and find consistency with the observed approximately 0.2 G field in the former case and the observed upper bound of approximately 0.2 G in the latter case. This resolves the controversy between the neutron diffraction and mu-spin relaxation experiments.

Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+delta

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.

Inhomogeneous magnetic-field response of YBa2Cu3Oy and La2-xSrxCuO4 persisting above the bulk superconducting transition temperature

We report that in YBa2Cu3Oy and La2-xSrxCuO4 there is a spatially inhomogeneous response to the magnetic field for temperatures T extending well above the bulk-superconducting transition temperature Tc. An inhomogeneous magnetic response is observed above Tc even in ortho-II YBa2Cu3O6.50, which has highly ordered doping. The degree of the field inhomogeneity above Tc tracks the hole-doping dependences of both Tc and the density of the superconducting carriers below Tc, and therefore is apparently coupled to superconductivity.

Absence of broken time-reversal symmetry in the pseudogap state of the high temperature La(2-x)SrxCuO4 superconductor from muon-spin-relaxation measurements

We have performed zero-field muon-spin-relaxation measurements on single crystals of La(2-x)SrxCuO4 to search for spontaneous currents in the pseudogap state. By comparing measurements on materials across the phase diagram, we put strict upper limits on any possible time-reversal symmetry breaking fields that could be associated with the pseudogap. Comparison between experimental limits and the proposed circulating current states effectively eliminates the possibility that such states exist in this family of materials.

Uncovering a pressure-tuned electronic transition in Bi(1.98)Sr(2.06)Y(0.68)Cu(2)O(8+delta) using Raman scattering and x-ray diffraction

We report pressure-tuned Raman and x-ray diffraction data of Bi(1.98.)Sr(2.06)Y(0.68)Cu(2)O(8+delta) revealing a critical pressure at 21 GPa with anomalies in electronic Raman background, electron-phonon coupling lambda, spectral weight transfer, density dependent behavior of phonons and magnons, and a compressibility change in the c axis. For the first time in a cuprate, mobile charge carriers, lattice, and magnetism all show anomalies at a distinct critical pressure in the same experimental setting. Furthermore, the spectral changes suggest that the critical pressure at 21 GPa is related to the critical point at optimal doping.

Time-reversal symmetry breaking by a (d+id) density-wave state in underdoped cuprate superconductors

It was proposed that the id(x(2)-y(2)) density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small d(xy) component to the DDW state breaks the symmetry between the counterpropagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a nonzero polar Kerr effect, which has recently been observed in the pseudogap phase.