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

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

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.

Short range smectic order driving long range nematic order: example of cuprates

We present a model for describing the combined presence of nematic and 'smectic' or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments on cuprates. The smectic order is treated as an electronic charge density wave with an associated Peierls distortion or a 'Pomeranchuk wave'. This primary order is restricted to nanoscale domains by disorder effects, while the secondary coupling to strain generates the nematic order with a considerably longer range. A variety of experimental results are shown to be consistent with our theoretical predictions.

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.

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.

Fermi-liquid computation of the phase diagram of high-Tc cuprate superconductors with an orbital antiferromagnetic pseudogap

A 4-parameter Fermi-liquid calculation of the high-Tc cuprate phase diagram is reported. Simultaneously accounted for are the special doping densities of 5% and 16%, the d-wave functional form of the (orbital antiferromagnetic) pseudogap, the measured Tc, superconducting gap, pseudogap and superfluid density as a function of doping, the particle-hole doping asymmetry and the half-filling spin wave velocity.

Multiscale distribution of oxygen puddles in 1/8 doped YBa2Cu3O6.67

Despite intensive research a physical explanation of high T_c superconductors remains elusive. One reason for this is that these materials have generally a very complex structure making useless theoretical models for a homogeneous system. Little is known on the control of the critical temperature by the space disposition of defects because of lack of suitable experimental probes. X-ray diffraction and neutron scattering experiments used to investigate y oxygen dopants in YBa₂Cu₃O_6+y lack of spatial resolution. Here we report the spatial imaging of dopants distribution inhomogeneity in YBa₂Cu₃O_6.67 using scanning nano X-ray diffraction. By changing the X-ray beam size from 1 micron to 300 nm of diameter, the lattice inhomogeneity increases. The ordered oxygen puddles size distribution vary between 6–8 nm using 1 × 1 μm² beam, while it is between 5–12 nm with a fat tail using the 300 × 300 nm² beam. The increased inhomogeneity at the nanoscale points toward a network of superconducting puddles made of ordered oxygen interstitials.

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.

Anomalous ordering in inhomogeneously strained materials

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of β=0.18±0.02, γ=1.0±0.1, and α=0.10±0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our simple model. We argue that the nature of the transition in our model is related to surface transitions although our model has no free surface.

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.