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.

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.

Critical nematic correlations throughout the superconducting doping range in Bi2-zPbzSr2-yLayCuO6+x

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-T_c superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi_2-zPb_zSr_2-yLa_yCuO_6+x. The ratio of the phase correlation length ξ_CDW to the orientation correlation length ξ_orient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.

Intersite Coulomb Interactions in Charge-Ordered Systems

Using ab initio approaches for extended Hubbard interactions coupled to phonons, we reveal that the intersite Coulomb interaction plays important roles in determining various distinctive phases of the paradigmatic charge-ordered materials of Ba_{1-x}K_{x}AO_{3} (A=Bi and Sb). We demonstrated that all their salient doping dependent experiment features such as breathing instabilities, anomalous phonon dispersions, and transition between charge-density wave and superconducting states can be accounted for very well if self-consistently obtained nearest neighbor Hubbard interactions are included, thus establishing a minimal criterion for reliable descriptions of spontaneous charge orders in solids.

Oxidation of Alcohols into Carbonyl Compounds Using a CuO@GO Nano Catalyst in Oxygen Atmospheres

In this article, the oxidation of alcohols into carbonyl compounds was studied in oxygen atmospheres using a copper oxide on graphene oxide (CuO@GO) nano composites catalyst, synthesized by the wet chemistry method. CuO@GO nano composites were prepared from GO, and CuO NPs by the sol-gel method. The transformation of aromatic alcohols into corresponding carbonyl compounds in good-to-high yields were observed using the CuO@GO catalyst under an oxygen atmosphere. Synthesized CuO@GO was confirmed by FT-IR, XRD, XPS, TEM, FE-SEM, TEM, and SEM analyses, and revealed intercalation of CuO-NPs on/in GO nano sheets through the chelation of Cu+2 ions with CO, COOH, and OH groups presenting on the GO nano sheets. The catalytic activity of CuO@GO nano composites for the conversion of alcohols into carbonyl compounds were evaluated through TOF (2.56 × 10−3 mol g−1 min−1). The use of CuO@GO has shown catalytic activity and recyclability with a high conversion of alcohols to ketones. We assume that the proposed CuO@GO catalyst can be used for other key organic transformations and will be evaluated in the future.

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.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

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.

Ground-state phase diagram of the t-t'-J model

We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

Extended Falicov-Kimball model: Hartree-Fock vs DMFT approach

In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal-insulator transitions found within the DMFT.

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.

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.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Enhancing the homogeneity of YBa2(Cu1−x Fe x )3O7−δsingle crystals by using an Fe-added Y2O3 crucible via top-seeded solution growth

Sizable metal-ion-doped YBa2Cu3O7−δ single crystals with high uniformity have been in great demand for fundamental studies on superconductivity. This article reports a novel approach, based on top-seeded solution growth and characterized by using an Fe-added Y2O3 crucible, to effectively enhance the homogeneity of YBa2(Cu1−x Fe x )3O7−δ single crystals. Because Fe ions are absorbable on or dissolvable from the Fe-Y2O3 crucible, it functions as a reservoir, yielding a stable Fe concentration in the liquid. Consequently, a series of acceptably sized YBa2(Cu1−x Fe x )3O7−δ single crystals with better uniformity than those grown by previous methods were obtained. The new dopant-added crucible, capable of balancing the solution spontaneously, is broadly applicable for preparing other doped single crystals.

Observation of two types of charge-density-wave orders in superconducting La2-xSrxCuO4

The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difficult to fully elucidate the relationship between the density wave orders and SC. Here, using resonant soft X-ray scattering, we study the archetypal cuprate La_2-xSr_xCuO₄ (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order with developing SDW stripe order near the superconducting T_c. These findings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO₂ planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders.

To fully elucidate the relationship between density wave orders and superconductivity in high-T_c cuprates remains difficult. Here, the authors reveal two types of charge-density-wave orders and their intertwined relationship with spin-density-wave order and superconductivity in La_2-xSr_xCuO_4.

Tc and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Strong long-range electron-phonon interaction as possible driving force for charge ordering in cuprates

A model resulting in charge ordering (CO) similar to that observed in cuprate superconductors is under study. It includes strong long-range electron-phonon interaction (EPI) and high density of correlated carriers. Coexistence of large bipolarons and delocalized carriers is a feature of such system. We develop generalized variation method to calculate the bipolaron size (CO period) in the ground normal state of such system at various doping. The approach allows the revealing of a possible physical reason of strongly different doping behavior of the CO wave vector in different cuprates. Obtained doping dependences of the CO period and temperature of the CO decay demonstrate quantitative agreement with those observed in cuprates. Predicted in the suggested approach ratio of the CO wave vector to the wave vector of the high-energy anomaly (HEA) in ARPES spectrum is in consent with that in cuprates. Calculated resonant x-rays scattering on the CO emerging in the model is in good agreement with experiments on cuprates including the asymmetry of the CO peaks' cross-section. A gap arises in the spectrum of delocalized carriers near antinodal direction due to their scattering on the periodic potential created by autolocalized carriers, analogously to photon crystal effect.

Disorder raises the critical temperature of a cuprate superconductor

With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of [Formula: see text] and observed a striking 50% increase of [Formula: see text], accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress [Formula: see text] Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in [Formula: see text] Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and [Formula: see text].

Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order

Fermi surface (FS) topology is a fundamental property of metals and superconductors. In electron-doped cuprate Nd_2-x Ce _x CuO₄ (NCCO), an unexpected FS reconstruction has been observed in optimal- and overdoped regime (x = 0.15-0.17) by quantum oscillation measurements (QOM). This is all the more puzzling because neutron scattering suggests that the antiferromagnetic (AFM) long-range order, which is believed to reconstruct the FS, vanishes before x = 0.14. To reconcile the conflict, a widely discussed external magnetic-field-induced AFM long-range order in QOM explains the FS reconstruction as an extrinsic property. Here, we report angle-resolved photoemission (ARPES) evidence of FS reconstruction in optimal- and overdoped NCCO. The observed FSs are in quantitative agreement with QOM, suggesting an intrinsic FS reconstruction without field. This reconstructed FS, despite its importance as a basis to understand electron-doped cuprates, cannot be explained under the traditional scheme. Furthermore, the energy gap of the reconstruction decreases rapidly near x = 0.17 like an order parameter, echoing the quantum critical doping in transport. The totality of the data points to a mysterious order between x = 0.14 and 0.17, whose appearance favors the FS reconstruction and disappearance defines the quantum critical doping. A recent topological proposal provides an ansatz for its origin.

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors

One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase (PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra (ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parameters with the total momentum of the Cooper pair to be zero and finite. The finite momentum pairing is accompanied with a spatial modulation of pairing order, i.e. a pair density wave (PDW). These PDW phases are intertwined with modulations of charge density and intra-unit cell form factors. The coexistence of the two different pairing orders provides the unique two-gaps like spectra observed by ARPES for superconducting cuprates. As temperature raises, the zero-momentum pairing order vanishes while the finite momentum pairing orders are kept, thus Fermi arcs are realized. The calculated quasiparticle spectra have the similar doping and temperature dependence as reported by ARPES and scanning tunneling spectroscopy (STS). The consequence of breaking symmetry between x and y due to the unidirectional PDW and the possibility to probe such a PDW state in the PG phase is discussed.

Hole pocket-driven superconductivity and its universal features in the electron-doped cuprates

After three decades of intensive research attention, the emergence of superconductivity in cuprates remains an unsolved puzzle. One major challenge has been to arrive at a satisfactory understanding of the unusual metallic "normal state" from which the superconducting state emerges upon cooling. A second challenge has been to achieve a unified understanding of hole- and electron-doped compounds. Here, we report detailed magnetoresistance measurements for the archetypal electron-doped cuprate Nd_2-x Ce _x CuO_4+δ that, in combination with previous data, provide crucial links between the normal and superconducting states and between the electron- and hole-doped parts of the phase diagram. The characteristics of the normal state (magnetoresistance, quantum oscillations, and Hall coefficient) and those of the superconducting state (superfluid density and upper critical field) consistently indicate two-band (electron and hole) features and point to hole pocket-driven superconductivity in these nominally electron-doped materials. We show that the approximate Uemura scaling between the superconducting transition temperature and the superfluid density found for hole-doped cuprates also holds for the small hole component of the superfluid density in electron-doped cuprates.

Nematicity and Charge Order in Superoxygenated La_{2-x}Sr_{x}CuO_{4+y}

In this Letter, we report a resonant x-ray scattering measurement of stripelike charge order in the 1/8th doped component of electronically phase-separated, orthorhombic La_{2}CuO_{4+y}. This observation is coupled to the absence of any resonant (001) peak, which at different resonant energies has been identified with the presence of low-temperature-tetragonal-like structural tilt patterns or nematicity in the CuO planes. Thus, we provide evidence that structural pinning is not necessary for the formation of static charge stripes and that the relationship between charge nematicity and stripes may not be simple.

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.

Relaxation of strongly coupled electron and phonon fields after photoemission and high-energy part of ARPES spectra of cuprates

An approach to considering systems with a high concentration of correlated carriers and strong long-range electron-phonon interaction and to calculating the high-energy part of the angle-resolved photoemission spectroscopy (ARPES) spectra of such systems is suggested. Joint relaxation of strongly coupled fields-a field of correlated electrons and phonon field-after photoemission is studied to clarify the nature of characteristic features observed in the high-energy part of the ARPES spectra of cuprate superconductors. Such relaxation occurs in systems with strong predominantly long-range electron-phonon interaction at sufficiently high carrier concentration due to the coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. It takes advantage of using the coherent states basis for the phonon field in the polaron and bipolaron states. The approach suggested yields all the high-energy spectral features like broad Gaussian band and regions of 'vertical dispersion' being in good quantitative agreement with the experiments on cuprates at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in superconducting cuprates changes the idea about their ground state above the superconducting transition temperature that is important for understanding transport and magnetic properties. High density of large-radius autolocalized carriers revealed may be a key to the explanation of charge ordering in doped cuprates.

Quasiparticle conductance-voltage characteristics for break junctions involving d-wave superconductors: charge-density-wave effects

Quasiparticle tunnel conductance-voltage characteristics (CVCs), [Formula: see text], were calculated for break junctions (BJs) made up of layered d-wave superconductors partially gapped by charge-density waves (CDWs). The current is assumed to flow in the ab-plane of electrodes. The influence of CDWs is analyzed by comparing the resulting CVCs with CVCs calculated for BJs made up of pure d-wave superconductors with relevant parameters. The main CDW-effects were found to be the appearance of new CVC peculiarities and the loss of CVC symmetry with respect to the V-sign. Tunnel directionality was shown to be one of the key factors in the formation of [Formula: see text] dependences. In particular, the orientation of electrodes with respect to the current channel becomes very important. As a result, [Formula: see text] can acquire a large variety of forms similar to those for tunnel junctions between superconductors with s-wave, d-wave, and mixed symmetry of their order parameters. The diversity of peculiarities is especially striking at finite temperatures. In the case of BJs made up of pure d-wave superconductors, the resulting CVC can include a two-peak gap-driven structure. The results were compared with the experimental BJ data for a number of high-T _c oxides. It was shown that the large variety of the observed current-voltage characteristics can be interpreted in the framework of our approach. Thus, quasiparticle tunnel currents in the ab-plane can be used as an additional mean to detect CDWs competing with superconductivity in cuprates or other layered superconductors.

Diversity of charge orderings in correlated systems

The phenomenon associated with inhomogeneous distribution of electron density is known as a charge ordering. In this work, we study the zero-bandwidth limit of the extended Hubbard model, which can be considered as a simple effective model of charge ordered insulators. It consists of the on-site interaction U and the intersite density-density interactions W_{1} and W_{2} between nearest neighbors and next-nearest neighbors, respectively. We derived the exact ground state diagrams for different lattice dimensionalities and discuss effects of small finite temperatures in the limit of high dimensions. In particular, we estimated the critical interactions for which new ordered phases emerge (laminar or stripe and four-sublattice-type). Our analysis show that the ground state of the model is highly degenerated. One of the most intriguing finding is that the nonzero temperature removes these degenerations.

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.

Mottness at finite doping and charge-instabilities in cuprates

The influence of the Mott physics on the doping-temperature phase diagram of copper oxides represents a major issue that is subject of intense theoretical and experimental effort. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p→Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping p_cr ≈0.16 irrespective of the temperature, and it can be well described by dynamical mean field theory calculations. We argue that the onset of the low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < p_cr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.

A practical superconducting-microcalorimeter X-ray spectrometer for beamline and laboratory science

We describe a series of microcalorimeter X-ray spectrometers designed for a broad suite of measurement applications. The chief advantage of this type of spectrometer is that it can be orders of magnitude more efficient at collecting X-rays than more traditional high-resolution spectrometers that rely on wavelength-dispersive techniques. This advantage is most useful in applications that are traditionally photon-starved and/or involve radiation-sensitive samples. Each energy-dispersive spectrometer is built around an array of several hundred transition-edge sensors (TESs). TESs are superconducting thin films that are biased into their superconducting-to-normal-metal transitions. The spectrometers share a common readout architecture and many design elements, such as a compact, 65 mK detector package, 8-column time-division-multiplexed superconducting quantum-interference device readout, and a liquid-cryogen-free cryogenic system that is a two-stage adiabatic-demagnetization refrigerator backed by a pulse-tube cryocooler. We have adapted this flexible architecture to mate to a variety of sample chambers and measurement systems that encompass a range of observing geometries. There are two different types of TES pixels employed. The first, designed for X-ray energies below 10 keV, has a best demonstrated energy resolution of 2.1 eV (full-width-at-half-maximum or FWHM) at 5.9 keV. The second, designed for X-ray energies below 2 keV, has a best demonstrated resolution of 1.0 eV (FWHM) at 500 eV. Our team has now deployed seven of these X-ray spectrometers to a variety of light sources, accelerator facilities, and laboratory-scale experiments; these seven spectrometers have already performed measurements related to their applications. Another five of these spectrometers will come online in the near future. We have applied our TES spectrometers to the following measurement applications: synchrotron-based absorption and emission spectroscopy and energy-resolved scattering; accelerator-based spectroscopy of hadronic atoms and particle-induced-emission spectroscopy; laboratory-based time-resolved absorption and emission spectroscopy with a tabletop, broadband source; and laboratory-based metrology of X-ray-emission lines. Here, we discuss the design, construction, and operation of our TES spectrometers and show first-light measurements from the various systems. Finally, because X-ray-TES technology continues to mature, we discuss improvements to array size, energy resolution, and counting speed that we anticipate in our next generation of TES-X-ray spectrometers and beyond.

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.

Electrical and thermal transport properties of the electron-doped cuprate Sm2-x Ce x CuO4-y system

Electrical and thermal transport measurements were performed on thin films of the electron-doped superconductor Sm_2-x Ce _x CuO_4-y (x  =  0.13  -  0.19) in order to study the evolving nature of the charge carriers from the under-doped to over-doped regime. A temperature versus cerium content (T  -  x) phase diagram has been constructed from the electrical transport measurements, yielding a superconducting region similar to that found for other electron-doped superconductors. Thermopower measurements show a dramatic change from the underdoped region (x  <  0.15) to the overdoped region (x  >  0.15). Application of the Fisher-Fisher-Huse (FFH) vortex glass scaling model to the magnetoresistance data was found to be insufficient to describe the data in the region of the vortex-solid to vortex-liquid transition. It was found instead that the modified vortex glass scaling model of Rydh, Rapp, and Anderson provided a good description of the data, indicating the importance of the applied field on the pinning landscape. A magnetic field versus temperature (H  -  T) phase diagram has also been constructed for the films with [Formula: see text], displaying the evolution of the vortex glass melting lines H _g (T) across the superconducting regime.

Influence of the spatially inhomogeneous gap distribution on the quasiparticle current in c-axis junctions involving d-wave superconductors with charge density waves

The quasiparticle tunnel current J(V) between the superconducting ab-planes along the c-axis and the corresponding conductance [Formula: see text] were calculated for symmetric junctions composed of disordered d-wave layered superconductors partially gapped by charge density waves (CDWs). Here, V is the voltage. Both the checkerboard and unidirectional CDWs were considered. It was shown that the spatial spread of the CDW-pairing strength substantially smears the peculiarities of G(V) appropriate to uniform superconductors. The resulting curves G(V) become very similar to those observed for a number of cuprates in intrinsic junctions, e.g. mesas. In particular, the influence of CDWs may explain the peak-dip-hump structures frequently found for high-T c oxides.

Remarkable Stability of Charge Density Wave Order in La_{1.875}Ba_{0.125}CuO_{4}

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾  h. We discuss the implications of these results for some of the competing theories.

Quasi-particle interference of heavy fermions in resonant x-ray scattering

Resonant x-ray scattering (RXS) has recently become an increasingly important tool for the study of ordering phenomena in correlated electron systems. Yet, the interpretation of RXS experiments remains theoretically challenging because of the complexity of the RXS cross section. Central to this debate is the recent proposal that impurity-induced Friedel oscillations, akin to quasi-particle interference signals observed with a scanning tunneling microscope (STM), can lead to scattering peaks in RXS experiments. The possibility that quasi-particle properties can be probed in RXS measurements opens up a new avenue to study the bulk band structure of materials with the orbital and element selectivity provided by RXS. We test these ideas by combining RXS and STM measurements of the heavy fermion compound CeMIn₅ (M = Co, Rh). Temperature- and doping-dependent RXS measurements at the Ce-M₄ edge show a broad scattering enhancement that correlates with the appearance of heavy f-electron bands in these compounds. The scattering enhancement is consistent with the measured quasi-particle interference signal in the STM measurements, indicating that the quasi-particle interference can be probed through the momentum distribution of RXS signals. Overall, our experiments demonstrate new opportunities for studies of correlated electronic systems using the RXS technique.

Charge density waves in strongly correlated electron systems

Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.

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.

Discovery of an Unconventional Charge Density Wave at the Surface of K_{0.9}Mo_{6}O_{17}

We use angle resolved photoemission spectroscopy, Raman spectroscopy, low energy electron diffraction, and x-ray scattering to reveal an unusual electronically mediated charge density wave (CDW) in K_{0.9}Mo_{6}O_{17}. Not only does K_{0.9}Mo_{6}O_{17} lack signatures of electron-phonon coupling, but it also hosts an extraordinary surface CDW, with T_{S_CDW}=220  K nearly twice that of the bulk CDW, T_{B_CDW}=115  K. While the bulk CDW has a BCS-like gap of 12 meV, the surface gap is 10 times larger and well in the strong coupling regime. Strong coupling behavior combined with the absence of signatures of strong electron-phonon coupling indicates that the CDW is likely mediated by electronic interactions enhanced by low dimensionality.

Observation of a three-dimensional quasi-long-range electronic supermodulation in YBa2Cu3O(7-x)/La0.7Ca0.3MnO3 heterostructures

Recent developments in high-temperature superconductivity highlight a generic tendency of the cuprates to develop competing electronic (charge) supermodulations. While coupled with the lattice and showing different characteristics in different materials, these supermodulations themselves are generally conceived to be quasi-two-dimensional, residing mainly in individual CuO₂ planes, and poorly correlated along the c axis. Here we observed with resonant elastic X-ray scattering a distinct type of electronic supermodulation in YBa₂Cu₃O_7−x (YBCO) thin films grown epitaxially on La_0.7Ca_0.3MnO₃ (LCMO). This supermodulation has a periodicity nearly commensurate with four lattice constants in-plane, eight out of plane, with long correlation lengths in three dimensions. It sets in far above the superconducting transition temperature and competes with superconductivity below this temperature for electronic states predominantly in the CuO₂ plane. Our finding sheds light on the nature of charge ordering in cuprates as well as a reported long-range proximity effect between superconductivity and ferromagnetism in YBCO/LCMO heterostructures.

Understanding the nature of competing phases is a key to understanding the superconducting mechanism of unconventional superconductors. Here, the authors demonstrate a three-dimensional charge ordering state which competes with superconductivity in epitaxial YBa₂Cu₃O_7-x thin films grown on La_0.7Ca_0.3MnO₃ substrates.

Direct observation of charge state in the quasi-one-dimensional conductor Li0.9Mo6O17

The quasi-one-dimensional conductor Li_0.9Mo₆O₁₇ has been of great interest because of its unusual properties. It has a conducting phase with properties different from a simple Fermi liquid, a poorly understood “insulating” phase as indicated by a metal-“insulator” crossover (a mystery for over 30 years), and a superconducting phase which may involve spin triplet Cooper pairs as a three-dimensional (p-wave) non-conventional superconductor. Recent evidence suggests a density wave (DW) gapping regarding the metal-“insulator” crossover. However, the nature of the DW, such as whether it is due to the change in the charge state or spin state, and its relationship to the dimensional crossover and to the spin triplet superconductivity, remains elusive. Here by performing ⁷Li-/⁹⁵Mo-nuclear magnetic resonance (NMR) spectroscopy, we directly observed the charge state which shows no signature of change in the electric field gradient (nuclear quadrupolar frequency) or in the distribution of it, thus providing direct experimental evidences demonstrating that the long mysterious metal-“insulator” crossover is not due to the charge density wave (CDW) that was thought, and the nature of the DW gapping is not CDW. This discovery opens a parallel path to the study of the electron spin state and its possible connections to other unusual properties.

Suppression of the antiferromagnetic pseudogap in the electron-doped high-temperature superconductor by protect annealing

In the hole-doped cuprates, a small number of carriers suppresses antiferromagnetism and induces superconductivity. In the electron-doped cuprates, on the other hand, superconductivity appears only in a narrow window of high-doped Ce concentration after reduction annealing, and strong antiferromagnetic correlation persists in the superconducting phase. Recently, Pr_1.3−xLa_0.7Ce_xCuO₄ (PLCCO) bulk single crystals annealed by a protect annealing method showed a high critical temperature of around 27 K for small Ce content down to 0.05. Here, by angle-resolved photoemission spectroscopy measurements of PLCCO crystals, we observed a sharp quasi-particle peak on the entire Fermi surface without signature of an antiferromagnetic pseudogap unlike all the previous work, indicating a dramatic reduction of antiferromagnetic correlation length and/or of magnetic moments. The superconducting state was found to extend over a wide electron concentration range. The present results fundamentally challenge the long-standing picture on the electronic structure in the electron-doped regime.

In cuprates, superconductivity exists in a narrow window at high electron doping concentration with strong antiferromagnetic correlations. Here, the authors demonstrate superconductivity with no effect of antiferromagnetic order in a cuprate for a wide electron doping range following a protect anneal process.

Uncertainty principle for experimental measurements: Fast versus slow probes

The result of a physical measurement depends on the time scale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to charge, spin or orbital instabilities combined with the disparity of the time scales associated to their fluctuations can lead to seemingly contradictory experimental findings. A particularly striking example is provided by systems of adatoms adsorbed on semiconductor surfaces where different experiments--angle-resolved photoemission, scanning tunneling microscopy and core-level spectroscopy--suggest different ordering phenomena. Using most recent first principles many-body techniques, we resolve this puzzle by invoking the time scales of fluctuations when approaching the different instabilities. These findings suggest a re-interpretation of ordering phenomena and their fluctuations in a wide class of solid-state systems ranging from organic materials to high-temperature superconducting cuprates.

Genesis of charge orders in high temperature superconductors

One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy.

The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction

Charge density wave (CDW) order appears throughout the underdoped high-temperature cuprate superconductors, but the underlying symmetry breaking and the origin of the CDW remain unclear. We use X-ray diffraction to determine the microscopic structure of the CDWs in an archetypical cuprate YBa₂Cu₃O_6.54 at its superconducting transition temperature ∼60 K. We find that the CDWs in this material break the mirror symmetry of the CuO₂ bilayers. The ionic displacements in the CDWs have two components, which are perpendicular and parallel to the CuO₂ planes, and are out of phase with each other. The planar oxygen atoms have the largest displacements, perpendicular to the CuO₂ planes. Our results allow many electronic properties of the underdoped cuprates to be understood. For instance, the CDWs will lead to local variations in the electronic structure, giving an explicit explanation of density-wave states with broken symmetry observed in scanning tunnelling microscopy and soft X-ray measurements.

Near to the superconducting state, cuprates display spatially-periodic charge density variations. Here, the authors use x-ray diffraction to determine the microscopic structure, showing how charge density waves in underdoped YBa₂Cu₃O_6.54 break the symmetry of the superconducting layers.

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields

Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured with x-ray scattering at zero and low fields. We combined a pulsed magnet with an x-ray free-electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields of up to 28 tesla. While the zero-field CDW order, which develops at temperatures below ~150 kelvin, is essentially two dimensional, at lower temperature and beyond 15 tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW appears around the zero-field superconducting transition temperature; in contrast, the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

Symmetry of charge order in cuprates

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.