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

Strain-induced long-range charge-density wave order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor

The mechanism of high-temperature superconductivity in copper oxides (cuprate) remains elusive, with the pseudogap phase considered a potential factor. Recent attention has focused on a long-range symmetry-broken charge-density wave (CDW) order in the underdoped regime, induced by strong magnetic fields. Here by 63,65Cu-nuclear magnetic resonance, we report the discovery of a long-range CDW order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor, induced by in-plane strain exceeding ∣ε∣ = 0.15 %, which deliberately breaks the crystal symmetry of the CuO2 plane. We find that compressive/tensile strains reduce superconductivity but enhance CDW, leaving superconductivity to coexist with CDW. The findings show that a long-range CDW order is an underlying hidden order in the pseudogap state, not limited to the underdoped regime, becoming apparent under strain. Our result sheds light on the intertwining of various orders in the cuprates.

Superconductivity due to fluctuating loop currents

Orbital magnetism and the loop currents (LCs) that accompany it have been proposed to emerge in many systems, including cuprates, iridates, and kagome superconductors. In the case of cuprates, LCs have been put forward as the driving force behind the pseudogap, strange-metal behavior, and dx2-y2-wave superconductivity. Here, we investigate whether fluctuating intra-unit-cell LCs can cause unconventional superconductivity. For odd-parity LCs, we find that they are repulsive in all pairing channels near the underlying quantum-critical point (QCP). For even-parity LCs, their fluctuations give rise to unconventional pairing, which is not amplified in the vicinity of the QCP, in sharp contrast to pairing mediated by spin-magnetic, nematic, or ferroelectric fluctuations. Applying our formalism to the cuprates, we conclude that fluctuating intra-unit-cell LCs are unlikely to yield dx2-y2-wave superconductivity. If LCs are to be relevant for the cuprates, they must break translation symmetry.

Strange Metals as Ersatz Fermi Liquids

A long-standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature (T). In this Letter we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency (ω) dependent conductivity satisfies ω/T scaling, we argue that the T-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are "ersatz Fermi liquids" with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion and time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes, which necessarily imply other exotic phenomena.

Time-reversal asymmetry without local moments via directional scalar spin chirality

Invariably, time-reversal symmetry (TRS) violation in a state of matter is identified with static magnetism in it. Here, a directional scalar spin chiral order (DSSCO) phase is introduced that disobeys this basic principle: it breaks TRS but has no density of static moments. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken TRS. Orbital moments are then precluded by the spatial symmetries of the spin rotation symmetric state. It is allowed in one, two and three dimensions under different conditions of temperature and disorder. Recently, polar Kerr effect experiments in the mysterious pseudogap phase of the underdoped cuprates hinted at a strange form of broken TRS below a temperature T _K, that exhibits a hysteretic 'memory effect' above T _K and begs reconciliation with nuclear magnetic resonance (which sees no moments), x-ray diffraction (which finds charge ordering tendencies) and the Nernst effect (which detects nematicity). Remarkably, the DSSCO provides a phenomenological route for reconciling all these observations, and it is conceivable that it onsets at the pseudogap temperature ∼T*. A six-spin interaction mediated by enhanced fluctuations of velocity asymmetry between left- and right-movers above the onset of charge ordering in the cuprates is proposed as the driving force behind DSSCO formation. A testable prediction of the existence of the DSSCO in the cuprates is a Kerr signal above T _K triggered and trainable by a current driven along one of the in-plane axes, but not by a current along the other.

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.

Contrasting Phenomenology of NMR Shifts in Cuprate Superconductors

Nuclear magnetic resonance (NMR) shifts, if stripped of their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu, a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hyperfine scenario used up to now is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field is perpendicular to the CuO 2 plane, which points to a localization of spin in the 3 d ( x 2 − y 2 ) orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.

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.

Perspective on the phase diagram of cuprate high-temperature superconductors

Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity the influential Uemura relation showed, early on, that the maximum critical temperature of superconductivity correlates with the density of the superfluid measured at low temperatures. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO2 plane, measured with nuclear magnetic resonance, reproduces this scaling. The charge transfer of the nominal copper hole to planar oxygen sets the maximum critical temperature. A three-dimensional phase diagram in terms of the charge content at copper as well as oxygen is introduced, which has the different cuprate families sorted with respect to their maximum critical temperature. We suggest that the critical temperature could be raised substantially if one were able to synthesize materials that lead to an increased planar oxygen hole content at the expense of that of planar copper.

Intra-unit-cell magnetic correlations near optimal doping in YBa2Cu3O6.85

The pseudo-gap phenomenon in copper oxide superconductors is central to any description of these materials as it prefigures the superconducting state itself. A magnetic intra-unit-cell order was found to occur just at the pseudo-gap temperature in four cuprate high-T_c superconducting families. Here we present polarized neutron-scattering measurements of nearly optimally doped YBa₂Cu₃O_6.85, carried out on two different spectrometers, that reveal several features. The intra-unit-cell order consists of finite-sized planar domains that are very weakly correlated along the c axis. At high temperature, only the out-of-plane magnetic components correlate, indicating a strong Ising anisotropy. An aditional in-plane response develops at low temperature, giving rise to an apparent tilt of the magnetic moment. The discovery of these two regimes puts stringent constraints, which are tightly bound to the pseudo-gap physics, on the intrinsic nature of intra-unit-cell order.

The pseudo-gap phenomenon is central to the description of high-T_c superconductivity in copper oxides. Here, the authors investigate nearly optimally doped YBCO using polarized neutron scattering to characterize intra-unit-cell magnetic correlations in relation with the pseudo-gap temperature.

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

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.