Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x

Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La1.65Eu0.2Sr0.15CuO4

Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant X-ray scattering on the (0 0 1) Bragg peak at the Cu [Formula: see text] and O [Formula: see text] resonances, we investigate nonequilibrium dynamics of [Formula: see text] nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La[Formula: see text]Eu[Formula: see text]Sr[Formula: see text]CuO[Formula: see text]. The orbital selectivity of the resonant X-ray scattering cross-section allows nematicity dynamics associated with the planar O 2[Formula: see text] and Cu 3[Formula: see text] states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.

Using strain to uncover the interplay between two- and three-dimensional charge density waves in high-temperature superconducting YBa2Cu3Oy

Uniaxial pressure provides an efficient approach to control charge density waves in YBa2Cu3Oy. It can enhance the correlation volume of ubiquitous short-range two-dimensional charge-density-wave correlations, and induces a long-range three-dimensional charge density wave, otherwise only accessible at large magnetic fields. Here, we use x-ray diffraction to study the strain dependence of these charge density waves and uncover direct evidence for a form of competition between them. We show that this interplay is qualitatively described by including strain effects in a nonlinear sigma model of competing superconducting and charge-density-wave orders. Our analysis suggests that strain stabilizes the 3D charge density wave in the regions between disorder-pinned domains of 2D charge density waves, and that the two orders compete at the boundaries of these domains. No signatures of discommensurations nor of pair density waves are observed. From a broader perspective, our results underscore the potential of strain tuning as a powerful tool for probing competing orders in quantum materials.

Universal Stripe Symmetry of Short-Range Charge Density Waves in Cuprate Superconductors

The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum- and yttrium-based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short-range CDW in bismuth-based cuprates. Here, high-resolution resonant inelastic x-ray scattering is employed to uncover the spatial symmetry of the CDW in Bi2 Sr2 - x Lax CuO6 + δ . Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real-space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°-rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe3Sn Kagome and Sn2 honeycomb layers. On the Fe3Sn layer terminated FeSn thin films epitaxially grown on SrTiO3(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5

The electronic instabilities in CsV₃Sb₅ are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV₃Sb₅, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L₁-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV₃Sb₅ go beyond the minimal framework of kagome electronic bands near van Hove filling.

Stabilization of three-dimensional charge order through interplanar orbital hybridization in PrxY1-xBa2Cu3O6+δ

The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\end{document}dx2−y2 orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using Cu L₃ and Pr M₅ resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa₂Cu₃O₇, where the Pr f-electrons create a direct orbital bridge between CuO₂ planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.

External perturbations can induce 3D charge order in cuprates, but the 3D correlation length is limited and the mechanism is not well understood. Ruiz et al. show that Pr substitution in YBa₂Cu₃O₇ enhances interplanar orbital coupling and stabilizes coherent 3D charge order that coexists with superconductivity.

Characterization of photoinduced normal state through charge density wave in superconducting YBa2Cu3O6.67

The normal state of high-T_c cuprates has been considered one of the essential topics in high-temperature superconductivity research. However, compared to the high magnetic field study of it, understanding a photoinduced normal state remains elusive. Here, we explore a photoinduced normal state of YBa₂Cu₃O_6.67 through a charge density wave (CDW) with time-resolved resonant soft x-ray scattering, as well as a high magnetic field x-ray scattering. In the nonequilibrium state where people predict a quenched superconducting state based on the previous optical spectroscopies, we experimentally observed a similar analogy to the competition between superconductivity and CDW shown in the equilibrium state. We further observe that the broken pairing states in the superconducting CuO₂ plane via the optical pump lead to nucleation of three-dimensional CDW precursor correlation. Ultimately, these findings provide a critical clue that the characteristics of the photoinduced normal state show a solid resemblance to those under magnetic fields in equilibrium conditions.

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy

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 YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), 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 = 6b 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.

Anomalous vortex liquid in charge-ordered cuprate superconductors

The magnetic-field scale at which superconducting vortices persist in underdoped cuprate superconductors has remained a controversial subject. Here we present an electrical transport study on three distinctly different cuprate families, at temperatures down to 0.32 K and magnetic fields up to 45 T. We reveal the presence of an anomalous vortex liquid state with a highly nonohmic resistivity in all three materials, irrespective of the level of disorder or structural details. The doping and field regime over which this anomalous vortex state persists suggests its occurrence is tied to the presence of long-range charge order under high magnetic field. Our results demonstrate that the intricate interplay between charge order and superconductivity can lead to an exotic vortex state.

The interplay between charge order and d-wave superconductivity in high-Tc cuprates remains an open question. While mounting evidence from spectroscopic probes indicates that charge order competes with superconductivity, to date little is known about the impact of charge order on charge transport in the mixed state, when vortices are present. Here we study the low-temperature electrical resistivity of three distinctly different cuprate families under intense magnetic fields, over a broad range of hole doping and current excitations. We find that the electronic transport in the doping regime where long-range charge order is known to be present is characterized by a nonohmic resistivity, the identifying feature of an anomalous vortex liquid. The field and temperature range in which this nonohmic behavior occurs indicates that the presence of long-range charge order is closely related to the emergence of this anomalous vortex liquid, near a vortex solid boundary that is defined by the excitation current in the T→ 0 limit. Our findings further suggest that this anomalous vortex liquid, a manifestation of fragile superconductivity with a suppressed critical current density, is ubiquitous in the high-field state of charge-ordered cuprates.

Surface/Interface Chemistry Engineering of Correlated-Electron Materials: From Conducting Solids, Phase Transitions to External-Field Response

Correlated electronic materials (CEMs) with strong electron-electron interactions are often associated with exotic properties, such as metal-insulator transition (MIT), charge density wave (CDW), superconductivity, and magnetoresistance (MR), which are fundamental to next generation condensed matter research and electronic devices. When the dimension of CEMs decreases, exposing extremely high specific surface area and enhancing electronic correlation, the surface states are equally important to the bulk phase. Therefore, surface/interface chemical interactions provide an alternative route to regulate the intrinsic properties of low-dimensional CEMs. Here, recent achievements in surface/interface chemistry engineering of low-dimensional CEMs are reviewed, using surface modification, molecule-solid interaction, and interface electronic coupling, toward modulation of conducting solids, phase transitions including MIT, CDW, superconductivity, and magnetism transition, as well as external-field response. Surface/interface chemistry engineering provides a promising strategy for exploring novel properties and functional applications in low-dimensional CEMs. Finally, the current challenge and outlook of the surface/interface engineering are also pointed out for future research development.

Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane

In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi₂Sr₂CaCu₂O_8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO₂ plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.

Knowledge of effective Coulomb interactions is central to understand emergent quantum phases in strongly correlated systems. Here, Boschini et al. report a dynamic quasi-circular spectrum of charge density wave fluctuations in the CuO₂ plane of Bi₂Sr₂CaCu₂O_8+δ, shedding a light on understanding how Coulomb interactions can lead to rotational and translational symmetry breaking in the cuprates.

Charge Density Waves in YBa_{2}Cu_{3}O_{6.67} Probed by Resonant X-Ray Scattering under Uniaxial Compression

We report a comprehensive Cu L_{3}-edge resonant x-ray scattering (RXS) study of two- and three-dimensional (2D and 3D) incommensurate charge correlations in single crystals of the underdoped high-temperature superconductor YBa_{2}Cu_{3}O_{6.67} under uniaxial compression up to 1% along the two inequivalent Cu─O─Cu bond directions (a and b) in the CuO_{2} planes. We confirm the strong in-plane anisotropy of the 2D charge correlations and observe their symmetric response to pressure: pressure along a enhances correlations along b, and vice versa. Our results imply that the underlying order parameter is uniaxial. In contrast, 3D long-range charge order is only observed along b in response to compression along a. Spectroscopic RXS measurements show that the 3D charge order resides exclusively in the CuO_{2} planes and may thus be generic to the cuprates. We discuss implications of these results for models of electronic nematicity and for the interplay between charge order and superconductivity.

Orbital symmetries of charge density wave order in YBa2Cu3O6+x

Charge density wave (CDW) order has been shown to compete and coexist with superconductivity in underdoped cuprates. Theoretical proposals for the CDW order include an unconventional d-symmetry form factor CDW, evidence for which has emerged from measurements, including resonant soft x-ray scattering (RSXS) in YBa₂Cu₃O_6+x (YBCO). Here, we revisit RSXS measurements of the CDW symmetry in YBCO, using a variation in the measurement geometry to provide enhanced sensitivity to orbital symmetry. We show that the (0 0.31 L) CDW peak measured at the Cu L edge is dominated by an s form factor rather than a d form factor as was reported previously. In addition, by measuring both (0.31 0 L) and (0 0.31 L) peaks, we identify a pronounced difference in the orbital symmetry of the CDW order along the a and b axes, with the CDW along the a axis exhibiting orbital order in addition to charge order.

Charge ordering in superconducting copper oxides

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ

High magnetic fields have revealed a surprisingly small Fermi surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of such a state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic-field measurements on the cuprate [Formula: see text]Cu[Formula: see text] to identify signatures of Fermi-surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap endpoint near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.

Spatially inhomogeneous competition between superconductivity and the charge density wave in YBa2Cu3O6.67

The charge density wave in the high-temperature superconductor YBa₂Cu₃O_7-x (YBCO) has two different ordering tendencies differentiated by their c-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDWs in neighbouring CuO₂ bilayers. This discovery has prompted several fundamental questions: how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use x-ray diffraction to study YBa₂Cu₃O_6.67 as a function of magnetic field and temperature. We show that regions with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations impact both the superconducting and normal state properties of YBCO.

Magnetic field-induced pair density wave state in the cuprate vortex halo

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N(r) within the halo surrounding Bi₂Sr₂CaCu₂O₈ vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N(r) modulations with wave vectors Q_P and 2Q _P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO₂ unit-cell periodicity and coexisting with its secondary CDWs.

Experimental station Bernina at SwissFEL: condensed matter physics on femtosecond time scales investigated by X-ray diffraction and spectroscopic methods

The Bernina instrument at the SwissFEL Aramis hard X-ray free-electron laser is designed for studying ultrafast phenomena in condensed matter and material science. Ultrashort pulses from an optical laser system covering a large wavelength range can be used to generate specific non-equilibrium states, whose subsequent temporal evolution can be probed by selective X-ray scattering techniques in the range 2-12 keV. For that purpose, the X-ray beamline is equipped with optical elements which tailor the X-ray beam size and energy, as well as with pulse-to-pulse diagnostics that monitor the X-ray pulse intensity, position, as well as its spectral and temporal properties. The experiments can be performed using multiple interchangeable endstations differing in specialization, diffractometer and X-ray analyser configuration and load capacity for specialized sample environment. After testing the instrument in a series of pilot experiments in 2018, regular user operation begins in 2019.

Uniaxial pressure control of competing orders in a high-temperature superconductor

Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa₂Cu₃O_6.67 under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along the a axis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.

Divergence of the quadrupole-strain susceptibility of the electronic nematic system YbRu2Ge2

A wide range of strongly correlated quantum materials, including some high-temperature superconductors, exhibit “electronic nematic” phases, in which the electronic properties spontaneously break the rotational symmetry of the crystal. However, the role that the corresponding nematic fluctuations play in these complicated systems is unclear, motivating the search for simpler model systems. Here, we identify a particular 4f intermetallic material which exhibits ferroquadrupole order, YbRu2Ge2, as just such a model system. We also provide a robust and accurate method to probe the divergence of an important associated quantity, the quadrupole-strain susceptibility. The temperature dependence of this quantity provides insight into the nature of the interactions that lead to ferroquadrupole order, in this case, magnetoelastic coupling.

Ferroquadrupole order associated with local 4f atomic orbitals of rare-earth ions is a realization of electronic nematic order. However, there are relatively few examples of intermetallic materials which exhibit continuous ferroquadrupole phase transitions, motivating the search for additional materials that fall into this category. Furthermore, it is not clear a priori whether experimental approaches based on transport measurements which have been successfully used to probe the nematic susceptibility in materials such as the Fe-based superconductors will be as effective in the case of 4f intermetallic materials, for which the important electronic degrees of freedom are local rather than itinerant and are consequently less strongly coupled to the charge-carrying quasiparticles near the Fermi energy. In the present work, we demonstrate that the intermetallic compound YbRu2Ge2 exhibits a tetragonal-to-orthorhombic phase transition consistent with ferroquadrupole order of the Yb ions and go on to show that elastoresistivity measurements can indeed provide a clear window on the diverging nematic susceptibility in this system. This material provides an arena in which to study the causes and consequences of electronic nematicity.

Light-Tunable 1T-TaS2 Charge-Density-Wave Oscillators

External stimuli-controlled phase transitions are essential for fundamental physics and design of functional devices. Charge density wave (CDW) is a metastable collective electronic phase featured by the periodic lattice distortion. Much attention has been attracted to study the external control of CDW phases. Although much work has been done in the electric-field-induced CDW transition, the study of the role of Joule heating in the phase transition is insufficient. Here, using the Raman spectroscopy, the electric-field-driven phase transition is in situ observed in the ultrathin 1T-TaS₂. By quantitative evaluation of the Joule heating effect in the electric-field-induced CDW transition, it is shown that Joule heating plays a secondary role in the nearly commensurate (NC) to incommensurate (IC) CDW transition, while it dominants the IC-NC CDW transition, providing a better understanding of the electric field-induced phase transition. More importantly, at room temperature, light illumination can modulate the CDW phase and thus tune the frequency of the ultrathin 1T-TaS₂ oscillators. This light tunability of the CDW phase transition is promising for multifunctional device applications.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Re-entrant charge order in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime

In the underdoped regime, the cuprate high-temperature superconductors exhibit a host of unusual collective phenomena, including unconventional spin and charge density modulations, Fermi surface reconstructions, and a pseudogap in various physical observables. Conversely, overdoped cuprates are generally regarded as conventional Fermi liquids possessing no collective electronic order. In partial contradiction to this widely held picture, we report resonant X-ray scattering measurements revealing incommensurate charge order reflections for overdoped (Bi,Pb)_2.12Sr_1.88CuO_6+δ (Bi2201), with correlation lengths of 40-60 lattice units, that persist up to temperatures of at least 250 K. The value of the charge order wavevector decreases with doping, in line with the extrapolation of the trend previously observed in underdoped Bi2201. In overdoped materials, however, charge order coexists with a single, unreconstructed Fermi surface without nesting or pseudogap features. The discovery of re-entrant charge order in Bi2201 thus calls for investigations in other cuprate families and for a reconsideration of theories that posit an essential relationship between these phenomena.

Stabilization of three-dimensional charge order in YBa2Cu3O6+x via epitaxial growth

Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa₂Cu₃O_6+x in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate 3D-CO in underdoped YBa₂Cu₃O_6+x films grown epitaxially on SrTiO₃ in the absence of magnetic fields. The resonance profiles indicate that Cu sites in the charge-reservoir layers participate in the CO state, and thus efficiently transmit CO correlations between adjacent CuO₂ bilayer units. The results offer fresh perspectives for experiments elucidating the influence of 3D-CO on the electronic properties of cuprates without the need to apply high magnetic fields.

In many cuprates the high temperature superconducting state competes with a charge ordered phase that has been difficult to investigate in detail. Here the authors show three-dimensional charge order can be stabilized in YBCO films and studied without using the high magnetic fields that are necessary in the bulk material.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below T _c, as well as in a wide temperature region above T _c, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T ^*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q  =  0 phase transitions, of both nematic and loop currents characters.

Fragility of Charge Order Near an Antiferromagnetic Quantum Critical Point

We investigate the interplay between charge order and superconductivity near an antiferromagnetic quantum critical point using sign-problem-free Quantum Monte Carlo simulations. We establish that, when the electronic dispersion is particle-hole symmetric, the system has an emergent SU(2) symmetry that implies a degeneracy between d-wave superconductivity and charge order with d-wave form factor. Deviations from particle-hole symmetry, however, rapidly lift this degeneracy, despite the fact that the SU(2) symmetry is preserved at low energies. As a result, we find a strong suppression of charge order caused by the competing, leading superconducting instability. Across the antiferromagnetic phase transition, we also observe a shift in the charge order wave vector from diagonal to axial. We discuss the implications of our results to the universal phase diagram of antiferromagnetic quantum-critical metals and to the elucidation of the charge order experimentally observed in the cuprates.

Charge Order and Superconductivity in Underdoped YBa_{2}Cu_{3}O_{7-δ} under Pressure

In underdoped cuprates, an incommensurate charge density wave (CDW) order is known to coexist with superconductivity. A dip in T_{c} at the hole doping level where the CDW is strongest (n_{p}≃0.12) suggests that CDW order may suppress superconductivity. We investigate the interplay of charge order with superconductivity in underdoped YBa_{2}Cu_{3}O_{7-δ} by measuring the temperature dependence of the Hall coefficient R_{H}(T) at high magnetic field and at high hydrostatic pressure. We find that, although pressure increases T_{c} by up to 10 K at 2.6 GPa, it has very little effect on R_{H}(T). This suggests that pressure, at these levels, only weakly affects the CDW and that the increase in T_{c} with pressure cannot be attributed to a suppression of the CDW. We argue, therefore, that the dip in T_{c} at n_{p}≃0.12 at ambient pressure is probably not caused by the CDW formation.

Spin susceptibility of charge-ordered YBa2Cu3O y across the upper critical field

The value of the upper critical field H_c2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-T_c copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use ¹⁷O NMR to measure the spin susceptibility [Formula: see text] of the CuO₂ planes at low temperature in charge-ordered YBa₂Cu₃O _y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest H_c2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces H_c2 in underdoped YBa₂Cu₃O _y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

Charge-density-wave order takes over antiferromagnetism in Bi2Sr2-x La x CuO6 superconductors

Superconductivity appears in the cuprates when a spin order is destroyed, while the role of charge is less known. Recently, charge density wave (CDW) was found below the superconducting dome in YBa₂Cu₃O_y when a high magnetic field is applied perpendicular to the CuO₂ plane, which was suggested to arise from incipient CDW in the vortex cores that becomes overlapped. Here by ⁶³Cu-nuclear magnetic resonance, we report the discovery of CDW induced by an in-plane field, setting in above the dome in single-layered Bi₂Sr_2−xLa_xCuO₆. The onset temperature T_CDW takes over the antiferromagnetic order temperature T_N beyond a critical doping level at which superconductivity starts to emerge, and scales with the pseudogap temperature T*. These results provide important insights into the relationship between spin order, CDW and the pseudogap, and their connections to high-temperature superconductivity.

Whilst superconductivity usually appears when magnetic order is suppressed, the role of charge is less known. Here, Kawasaki et al. report a charge density wave (CDW) above the superconducting transition induced by an in-plane magnetic field in Bi₂Sr_2-xLa_xCuO₆, with the CDW onset temperature scaling with the pseudogap temperature.

Dimensional Crossover of Charge-Density Wave Correlations in the Cuprates

Short-range charge-density wave correlations are ubiquitous in underdoped cuprates. They are largely confined to the copper-oxygen planes and typically oscillate out of phase from one unit cell to the next in the c direction. Recently, it was found that a considerably longer-range charge-density wave order develops in YBa_{2}Cu_{3}O_{6+x} above a sharply defined crossover magnetic field. This order is more three-dimensional and is in-phase along the c axis. Here, we show that such behavior is a consequence of the conflicting ordering tendencies induced by the disorder potential and the Coulomb interaction, where the magnetic field acts to tip the scales from the former to the latter. We base our conclusion on analytic large-N analysis and Monte Carlo simulations of a nonlinear sigma model of competing superconducting and charge-density wave orders. Our results are in agreement with the observed phenomenology in the cuprates, and we discuss their implications to other members of this family, which have not been measured yet at high magnetic fields.

Local particle-hole pair excitations by SU(2) symmetry fluctuations

Understanding the pseudo-gap phase which opens in the under-doped regime of cuprate superconductors is one of the most enduring challenges of the physics of these compounds. A depletion in the electronic density of states is observed, which is gapping out part of the Fermi surface, leading to the formation of mysterious lines of massless excitations- the Fermi arcs. Here we give a new theoretical account of the physics of the pseudo-gap phase in terms of the emergence of local patches of particle-hole pairs generated by SU(2) symmetry fluctuations. The proliferation of these local patches accounts naturally for the robustness of the pseudo-gap phase to disturbances like disorder or magnetic field and is shown to gap out part of the Fermi surface, leading to the formation of the Fermi arcs. Most noticeably, we show that these patches induce a modulated charge distribution on the Oxygen atoms, in remarkable agreement with recent X-ray and STM observations.

Neutron scattering by Dirac multipoles

Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-T _c superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments. We report magnetic scattering amplitudes for diffraction by polar multipoles that have universal value, because they are not specific to ceramic superconductors. To illustrate this attribute, we consider neutron Bragg diffraction from a magnetically ordered iridate (Sr₂IrO₄) and discuss shortcomings in published interpretations of diffraction data.

Quasiparticle Scattering off Defects and Possible Bound States in Charge-Ordered YBa_{2}Cu_{3}O_{y}

We report the NMR observation of a skewed distribution of ^{17}O Knight shifts when a magnetic field quenches superconductivity and induces long-range charge-density-wave (CDW) order in YBa_{2}Cu_{3}O_{y}. This distribution is explained by an inhomogeneous pattern of the local density of states N(E_{F}) arising from quasiparticle scattering off, yet unidentified, defects in the CDW state. We argue that the effect is most likely related to the formation of quasiparticle bound states, as is known to occur, under specific circumstances, in some metals and superconductors (but not in the CDW state, in general, except for very few cases in 1D materials). These observations should provide insight into the microscopic nature of the CDW, especially regarding the reconstructed band structure and the sensitivity to disorder.

Ideal charge-density-wave order in the high-field state of superconducting YBCO

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa₂Cu₃O₂ (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field ([Formula: see text]) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO₂ planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to [Formula: see text], given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an "ideal" disorder-free cuprate.

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8

Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that, inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations [Doiron-Leyraud N, et al. (2007) Nature 447(7144):565-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110(15):5774-5778], and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys Rev B 93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa₂Cu₄O₈ that are consistent with a T² resistivity extending down to 1.5 K. The magnitude of the T² coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.

Magnetic phase diagram of underdoped YBa2Cu3O y inferred from torque magnetization and thermal conductivity

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa₂Cu₃O _y was obtained by NMR and resonant X-ray scattering. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D charge-density-wave (CDW) formation with long-range order (LRO) was observed by X-ray diffraction in [Formula: see text] 15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity [Formula: see text] to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and [Formula: see text] at the fields [Formula: see text] and [Formula: see text], which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field [Formula: see text] of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (41 T), the second vortex solid melts to a vortex liquid which survives to fields well above 41 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field [Formula: see text].

The amplitudes and the structure of the charge density wave in YBCO

We find unknown s- and d-wave amplitudes of the recently discovered charge density wave (CDW) in underdoped cuprates. To do so we perform a combined analysis of experimental data for ortho-II YBa₂Cu₃O_y. The analysis includes data on nuclear magnetic resonance, resonant inelastic X-ray scattering, and hard X-ray diffraction. The amplitude of doping modulation found in our analysis is 3.5 · 10⁻³ in a low magnetic field and T = 60 K, the amplitude is 6.5 · 10⁻³ in a magnetic field of 30T and T = 1.3 K. The values are in units of elementary charge per unit cell of a CuO₂ plane. We show that the data rule out a checkerboard pattern, and we also show that the data might rule out mechanisms of the CDW which do not include phonons.

Doping-dependent charge order correlations in electron-doped cuprates

Understanding the interplay between charge order (CO) and other phenomena (for example, pseudogap, antiferromagnetism, and superconductivity) is one of the central questions in the cuprate high-temperature superconductors. The discovery that similar forms of CO exist in both hole- and electron-doped cuprates opened a path to determine what subset of the CO phenomenology is universal to all the cuprates. We use resonant x-ray scattering to measure the CO correlations in electron-doped cuprates (La2-x Ce x CuO4 and Nd2-x Ce x CuO4) and their relationship to antiferromagnetism, pseudogap, and superconductivity. Detailed measurements of Nd2-x Ce x CuO4 show that CO is present in the x = 0.059 to 0.166 range and that its doping-dependent wave vector is consistent with the separation between straight segments of the Fermi surface. The CO onset temperature is highest between x = 0.106 and 0.166 but decreases at lower doping levels, indicating that it is not tied to the appearance of antiferromagnetic correlations or the pseudogap. Near optimal doping, where the CO wave vector is also consistent with a previously observed phonon anomaly, measurements of the CO below and above the superconducting transition temperature, or in a magnetic field, show that the CO is insensitive to superconductivity. Overall, these findings indicate that, although verified in the electron-doped cuprates, material-dependent details determine whether the CO correlations acquire sufficient strength to compete for the ground state of the cuprates.

Single reconstructed Fermi surface pocket in an underdoped single-layer cuprate superconductor

The observation of a reconstructed Fermi surface via quantum oscillations in hole-doped cuprates opened a path towards identifying broken symmetry states in the pseudogap regime. However, such an identification has remained inconclusive due to the multi-frequency quantum oscillation spectra and complications accounting for bilayer effects in most studies. We overcome these impediments with high-resolution measurements on the structurally simpler cuprate HgBa₂CuO_4+δ (Hg1201), which features one CuO₂ plane per primitive unit cell. We find only a single oscillatory component with no signatures of magnetic breakdown tunnelling to additional orbits. Therefore, the Fermi surface comprises a single quasi-two-dimensional pocket. Quantitative modelling of these results indicates that a biaxial charge density wave within each CuO₂ plane is responsible for the reconstruction and rules out criss-crossed charge stripes between layers as a viable alternative in Hg1201. Lastly, we determine that the characteristic gap between reconstructed pockets is a significant fraction of the pseudogap energy.

The identification of broken symmetry states in underdoped cuprate superconductors via quantum oscillation measurements remains inconclusive. Here, Chan et al. report the reconstructed Fermi surface of HgBa₂CuO_4+δ comprises only a single pocket indicating a biaxial charge-density-wave order within each CuO₂ plane.