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

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa2Cu3O y

The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (μSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa₂Cu₃O _y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures T_mag ≈ T*. The absence of any static field (to which μSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at T_mag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

Pseudogap in cuprates in the loop-current ordered state

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors [Formula: see text], the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the [Formula: see text] directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the 'edge' of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the 'ordered' phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

Absence of static loop-current magnetism at the apical oxygen site in HgBa2CuO4+δ from NMR

The simple structure of HgBa(2)CuO(4+δ) (Hg1201) is ideal among cuprates for study of the pseudogap phase as a broken symmetry state. We have performed (17)O nuclear magnetic resonance on an underdoped Hg1201 crystal with a transition temperature of 74 K to look for circulating loop currents proposed theoretically and inferred from neutron scattering. The narrow spectra preclude static local fields in the pseudogap phase at the apical site, suggesting that the moments observed with neutrons are fluctuating. The nuclear magnetic resonance frequency shifts are consistent with a dipolar field from the Cu(2+) site.

Absence of orbital currents in superconducting YBa2Cu4O8 using a zeeman-perturbed nuclear-quadrupole-resonance technique

Zeeman perturbed nuclear quadrupole resonance was applied to evaluate weak magnetic fields in the context of orbital currents in cuprate superconductors. The magnetic environment of the barium atom in c-axis oriented powder samples of YBa(2)Cu(4)O(8) was investigated in the pseudogap phase at 90 K. No evidence for orbital currents was found: any static and dynamic field must be less than 0.07 and 0.7 mT, respectively.

Direct search for a ferromagnetic phase in a heavily overdoped nonsuperconducting copper oxide

The doping of charge carriers into the CuO(2) planes of copper oxide Mott insulators causes a gradual destruction of antiferromagnetism and the emergence of high-temperature superconductivity. Optimal superconductivity is achieved at a doping concentration p beyond which further increases in doping cause a weakening and eventual disappearance of superconductivity. A potential explanation for this demise is that ferromagnetic fluctuations compete with superconductivity in the overdoped regime. In this case, a ferromagnetic phase at very low temperatures is predicted to exist beyond the doping concentration at which superconductivity disappears. Here we report on a direct examination of this scenario in overdoped La(2-x)Sr(x)CuO(4) using the technique of muon spin relaxation. We detect the onset of static magnetic moments of electronic origin at low temperature in the heavily overdoped nonsuperconducting region. However, the magnetism does not exist in a commensurate long-range ordered state. Instead it appears as a dilute concentration of static magnetic moments. This finding places severe restrictions on the form of ferromagnetism that may exist in the overdoped regime. Although an extrinsic impurity cannot be absolutely ruled out as the source of the magnetism that does occur, the results presented here lend support to electronic band calculations that predict the occurrence of weak localized ferromagnetism at high doping.

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.

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.