Impact of quenched oxygen disorder on charge density wave order in YBa2Cu3O6+x

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.

Enhanced charge density wave coherence in a light-quenched, high-temperature superconductor

Superconductivity and charge density waves (CDWs) are competitive, yet coexisting, orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scale is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa₂Cu₃O_6+x after the quench of superconductivity by an infrared laser pulse. We observe a nonthermal response of the CDW order characterized by a near doubling of the correlation length within ≈1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDWs manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations.

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.

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.

c-Oriented YBa2Cu3O7−δ film with embedded a-oriented grains grown by liquid phase epitaxy under fine-tuning supersaturation

The performance of superconductor films is related to their crystallographic orientations, which are strongly dependent on the supersaturation (σ) in the solution used for liquid phase epitaxy (LPE). To date, except for two extreme states, low and high σ for the preparation of a- and c-axis-oriented YBa2Cu3O7−δ films, respectively, little attention has been directed toward intermediate σ, which is of great importance for achieving a variety of artificial microstructures that are in principle difficult to obtain by existing crystal growth methods. Here, a further step is taken towards the comprehension of how the crystallographic orientations and microstructure are correlated with supersaturation. Fine-tuning of σ to an intermediate state is realized by introducing an additional factor, namely the holding time, that adjusts the initially uncertain state to a certain and stable one. This factor is controlled along with the commonly used variables of the amount of fresh solvent material and the melting time. Consequently, for the first time, a composite epitaxial microstructure of a c-axis-oriented YBa2Cu3O7−δ film with embedded a-axis grains on a (110) NdGaO3 substrate was successfully grown by LPE. The epitaxial interface between a- and c-axis grains potentially serves as a flux pinning site. This work provides further insights into how control of artificial microstructures can be used to enhance superconducting properties.

Collective Dynamics and Strong Pinning near the Onset of Charge Order in La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4}

The dynamics of charge-ordered states is one of the key issues in underdoped cuprate high-temperature superconductors, but static short-range charge-order (CO) domains have been detected in almost all cuprates. We probe the dynamics across the CO (and structural) transition in La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4} by measuring nonequilibrium charge transport, or resistance R as the system responds to a change in temperature and to an applied magnetic field. We find evidence for metastable states, collective behavior, and criticality. The collective dynamics in the critical regime indicates strong pinning by disorder. Surprisingly, nonequilibrium effects, such as avalanches in R, are revealed only when the critical region is approached from the charge-ordered phase. Our results on La_{1.48}Nd_{0.4}Sr_{0.12}CuO_{4} provide the long-sought evidence for the fluctuating order across the CO transition, and also set important constraints on theories of dynamic stripes.

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.

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.

Nanoscale electrodynamics of strongly correlated quantum materials

Electronic, magnetic, and structural phase inhomogeneities are ubiquitous in strongly correlated quantum materials. The characteristic length scales of the phase inhomogeneities can range from atomic to mesoscopic, depending on their microscopic origins as well as various sample dependent factors. Therefore, progress with the understanding of correlated phenomena critically depends on the experimental techniques suitable to provide appropriate spatial resolution. This requirement is difficult to meet for some of the most informative methods in condensed matter physics, including infrared and optical spectroscopy. Yet, recent developments in near-field optics and imaging enabled a detailed characterization of the electromagnetic response with a spatial resolution down to 10 nm. Thus it is now feasible to exploit at the nanoscale well-established capabilities of optical methods for characterization of electronic processes and lattice dynamics in diverse classes of correlated quantum systems. This review offers a concise description of the state-of-the-art near-field techniques applied to prototypical correlated quantum materials. We also discuss complementary microscopic and spectroscopic methods which reveal important mesoscopic dynamics of quantum materials at different energy scales.

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.

Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime

Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a₀) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector Q_A of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at [Formula: see text] throughout the underdoped phase diagram of the canonical cuprate Bi₂Sr₂CaCu₂O₈ These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

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

The application of magnetic fields to layered cuprates suppresses their high-temperature superconducting behaviour and reveals competing ground states. In widely studied underdoped YBa2Cu3O6+x (YBCO), the microscopic nature of field-induced electronic and structural changes at low temperatures remains unclear. Here we report an X-ray study of the high-field charge density wave (CDW) in YBCO. For hole dopings ∼0.123, we find that a field (B∼10 T) induces additional CDW correlations along the CuO chain (b-direction) only, leading to a three-dimensional (3D) ordered state along this direction at B∼15 T. The CDW signal along the a-direction is also enhanced by field, but does not develop an additional pattern of correlations. Magnetic field modifies the coupling between the CuO2 bilayers in the YBCO structure, and causes the sudden appearance of the 3D CDW order. The mirror symmetry of individual bilayers is broken by the CDW at low and high fields, allowing Fermi surface reconstruction, as recently suggested.

Magnetostriction and Magnetostructural Domains in Antiferromagnetic YBa2Cu3O6

We use high-resolution neutron Larmor diffraction and capacitative dilatometry to investigate spontaneous and forced magnetostriction in undoped, antiferromagnetic YBa_{2}Cu_{3}O_{6.0}, the parent compound of a prominent family of high-temperature superconductors. Upon cooling below the Néel temperature T_{N}=420  K, Larmor diffraction reveals the formation of magnetostructural domains of characteristic size ∼240  nm. In the antiferromagnetic state, dilatometry reveals a minute (4×10^{-6}) orthorhombic distortion of the crystal lattice in external magnetic fields. We attribute these observations to exchange striction and spin-orbit coupling induced magnetostriction, respectively, and show that they have an important influence on the thermal and charge transport properties of undoped and lightly doped cuprates.

Superconductivity. Broken translational and rotational symmetry via charge stripe order in underdoped YBa₂Cu₃O(6+y)

After the discovery of stripelike order in lanthanum-based copper oxide superconductors, charge-ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between unidirectional (stripes) and bidirectional (checkerboard) charge order in yttrium- and bismuth-based materials. We used resonant x-ray scattering to measure the two-dimensional structure factor in the superconductor YBa2Cu3O(6+y) in reciprocal space. Our data reveal the presence of charge stripe order (i.e., locally unidirectional density waves), which may represent the true microscopic nature of charge modulation in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across the stripes than along them, which provides additional evidence for the intrinsic unidirectional nature of the charge order.

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

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