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In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW’s microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa 2 Cu 3 O y is unidirectional with a commensurate period of three unit cells ( λ  = 3 b ), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ  = 6 b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice. Understanding cuprate superconductors requires better knowledge of the microscopic structure of their charge-density waves (CDW). Here, the authors report evidence that the long-range CDW order in YBa 2 Cu 3 O y has a local commensurate period of three unit cells.

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 YBa 2 Cu 3 O y 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 NbSe 2 , 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. The nature and universality of the ordering phenomena observed in the normal state of high-temperature superconductors remain unclear. Here, Wu et al . observe several aspects of incipient charge ordering in YBCO via NMR measurements, clarifying the role of quenched disorder in their emergence.

Charge-stripe order and superconductivity Nuclear magnetic resonance measurements of the model high-temperature copper oxide superconductor YBa 2 Cu 3 O y demonstrate that high magnetic fields induce charge order, without spin order, within the material's CuO 2 planes. The observed charge order has characteristics similar to those of stripe-ordered copper oxides, in which electronic charges spontaneously organize themselves into 'stripes'. The charge order develops only when superconductivity fades away. This work suggests that stripes are more common objects in the cuprates than was thought. They seem to compete with superconductivity, although the tendency to form stripes may be a necessary ingredient of high temperature superconductivity. Electronic charges introduced in copper-oxide (CuO 2 ) planes generate high-transition-temperature ( T c ) superconductivity but, under special circumstances, they can also order into filaments called stripes 1 . Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues 2 , 3 . To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations 4 , 5 , 6 in YBa 2 Cu 3 O y (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order 7 , 8 , 9 . Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO 2 planes of YBa 2 Cu 3 O y . The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4 a -periodic modulation as in stripe-ordered copper oxides 1 . That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La 2− x Ba x CuO 4 (ref.  1 ) suggests that charge order, although visibly pinned by CuO chains in YBa 2 Cu 3 O y , is an intrinsic propensity of the superconducting planes of high- T c copper oxides.

X-ray diffraction experiments reveal that spatial charge ordering occurs in the pseudogap state of YBa 2 Cu 3 O 6.67 . Moreover, this charge ordered state competes with high-temperature superconductivity, and their relative strengths can be tuned using a magnetic field. Superconductivity often emerges in the proximity of, or in competition with, symmetry-breaking ground states such as antiferromagnetism or charge density waves 1 , 2 , 3 , 4 , 5 (CDW). A number of materials in the cuprate family, which includes the high transition-temperature (high- T c ) superconductors, show spin and charge density wave order 5 , 6 , 7 . Thus a fundamental question is to what extent do these ordered states exist for compositions close to optimal for superconductivity. Here we use high-energy X-ray diffraction to show that a CDW develops at zero field in the normal state of superconducting YBa 2 Cu 3 O 6.67 ( T c  = 67 K). This sample has a hole doping of 0.12 per copper and a well-ordered oxygen chain superstructure 8 . Below T c , the application of a magnetic field suppresses superconductivity and enhances the CDW. Hence, the CDW and superconductivity in this typical high- T c material are competing orders with similar energy scales, and the high- T c superconductivity forms from a pre-existing CDW environment. Our results provide a mechanism for the formation of small Fermi surface pockets 9 , which explain the negative Hall and Seebeck effects 10 , 11 and the ‘ T c plateau’ 12 in this material when underdoped.

A thermodynamic probe of the recently discovered charge-density-wave order in YBa 2 Cu 3 O y reveals a biaxial modulation in magnetic fields up to 40 T. The interplay between superconductivity and any other competing order is an essential part of the long-standing debate on the origin of high-temperature superconductivity in cuprate materials 1 , 2 . Akin to the situation in the heavy fermions, organic superconductors and pnictides, it has been proposed that the pairing mechanism in the cuprates comes from fluctuations of a nearby quantum phase transition 3 . Recent evidence for charge modulation 4 and its associated fluctuations 5 , 6 , 7 in the pseudogap phase of YBa 2 Cu 3 O y makes charge order a likely candidate for a competing order. However, a thermodynamic signature of the charge-ordering phase transition is still lacking. Moreover, whether the charge modulation is uniaxial or biaxial remains controversial. Here we address both issues by measuring sound velocities in YBa 2 Cu 3 O 6.55 in high magnetic fields. We provide the first thermodynamic signature of the competing charge-order phase transition in YBa 2 Cu 3 O y and construct a field–temperature phase diagram. The comparison of different acoustic modes indicates that the charge modulation is biaxial, which differs from a uniaxial stripe charge order.

The thermal diffusivity in the ab plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25–300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron–phonon “soup” picture characterized by a diffusion constant D ~ v B 2 τ , where vB is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time τ ∼ ħ/kBT.

The application of magnetic fields to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa 2 Cu 3 O 6+ x (YBCO), the microscopic nature of field-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-field charge density wave (CDW) in YBCO. For hole dopings ∼0.123, we find that a field ( B ∼10 T) induces additional CDW correlations along the CuO chain ( b -direction) only, leading to a three-dimensional (3D) ordered state along this direction at B ∼15 T. The CDW signal along the a -direction is also enhanced by field, but does not develop an additional pattern of correlations. Magnetic field modifies the coupling between the CuO 2 bilayers in the YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing Fermi surface reconstruction, as recently suggested. The interplay between competing orders in high-temperature superconductors can be tuned by the application of magnetic fields. Here, Chang et al . report high field induced three-dimensional charge density wave in underdoped YBa 2 Cu 3 O 6.67 , which suggests Fermi surface reconstruction due to competing orders.

In many high temperature superconductors, small orthorhombic distortions of the lattice structure result in surprisingly large symmetry breaking of the electronic states and macroscopic properties, an effect often referred to as nematicity. To directly study the impact of symmetry-breaking lattice distortions on the electronic states, using low-temperature scanning tunnelling microscopy we image at the atomic scale the influence of strain-tuned lattice distortions on the correlated electronic states in the iron-based superconductor LiFeAs, a material which in its ground state is tetragonal with four-fold ( C 4 ) symmetry. Our experiments uncover a new strain-stabilised modulated phase which exhibits a smectic order in LiFeAs, an electronic state which not only breaks rotational symmetry but also reduces translational symmetry. We follow the evolution of the superconducting gap from the unstrained material with C 4 symmetry through the new smectic phase with two-fold ( C 2 ) symmetry and charge-density wave order to a state where superconductivity is completely suppressed. Small structural distortions may lead to dramatic modification in the electronic states in strong correlated materials. Here, Yim et al. image a strain-stabilized smectic electronic order in LiFeAs with both broken rotational symmetry and reduced translational symmetry.

Broken symmetry in the pseudogap phase Knowledge of the nature of the pseudogap phase is critical to understanding the properties of high-transition-temperature (high- T c ) copper oxide superconductors. A fundamental question is what symmetries are broken when that phase sets in below a certain temperature, T *. Daou et al . 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. They 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. They conclude that the pseudogap phase is an electronic state that strongly breaks fourfold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order. In the study of high-transition-temperature (high- T c ) copper oxide superconductors, a fundamental question is what symmetries are broken when the pseudogap phase sets in below a temperature T *. A large in-plane anisotropy of the Nernst effect is now observed in a high- T c copper oxide superconductor that sets in precisely at T * throughout the doping phase diagram. It is concluded that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. 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 1 . 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 2 , 3 and the polar Kerr effect 4 that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements 5 and inelastic neutron scattering 6 , 7 , 8 at low doping, and from scanning tunnelling spectroscopy 9 , 10 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 11 , 12 .

Evidence is mounting that charge order competes with superconductivity in high T c cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa 2 Cu 3 O y has maximum strength inside the superconducting dome, similar to compounds of the La 2− x (Sr,Ba) x CuO 4 family. In YBa 2 Cu 3 O y , this occurs at doping levels of p =0.11–0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi 2 Sr 2 CaCu 2 O 8+ δ , can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state. The recent discovery of charge order in YBa 2 Cu 3 O y was unexpected. A systematic study of the evolution of this phenomenon as a function of magnetic field conducted by Wu et al . reveals how the competition between charge order and superconductivity may actually be universal to the underdoped cuprates.