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

Enhancement of magnetism by tailoring synthesis conditions in electron-doped superconducting nanoparticles

A study on the effects of sample synthesis conditions on the particle size, structure, and magnetic properties of electron-doped cuprate superconductors of Eu1.85Ce0.15CuO4+α-δ (ECCO) nanoparticles has been carried out using transmission electron microscopy (TEM), X-ray diffraction (XRD) and the superconducting quantum interference device magnetometer (SQUID). The ECCO nanoparticles were prepared through the sol-gel method with various sintering and annealing temperatures. From TEM characterization, the average particle sizes are 87 nm and 103 nm for the sintering temperatures of 700 °C and 900 °C, respectively. The XRD results with structural Rietveld refinement reveal that the lattice constants and bond distance Cu-O change considerably compared to the bulk case. Reducing the particle and crystallite size to below 200 nm causes strong suppression in the superconducting state. From SQUID measurements it is found that none of the samples show superconducting behavior. An upturn in magnetic susceptibility below 10 K is observed in the sample when the crystallite size is in the range of 69 nm to 88 nm, indicating the existence of magnetism. The lower the sintering temperature of the sample synthesis, the higher the effective magnetic moment and Curie temperature. It suggests that the magnetic correlation is more developed in the smaller samples.

Superconducting and charge-ordered states in the anisotropic t-J-U model

Motivated by the effect of symmetry breaking in cuprates superconductors YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text], we employ the renormalized mean-field theory to study the presence of uniform superconducting and charge-ordered states in two anisotropic t-J-U models, either with hopping strength anisotropy or antiferromagnetic interaction anisotropy. In the case of uniform superconducting state, compared with the isotropic t-J-U model with only [Formula: see text]-wave superconducting state, there is an additional s-wave superconducting state in the model with hopping strength anisotropy. Meanwhile, the hopping anisotropy may enhance the critical Coulomb interaction [Formula: see text] at the Mott insulator to the Gossamer superconductor transition point, and strong hopping anisotropy may weaken the superconducting state. In the case of a charge-ordered state, hopping anisotropy may suppress the amplitude of the charge density waves and pair density waves, which originate from local Coulomb interactions. These results indicate that the effects of hopping anisotropy and local Coulomb interactions are competitive. Moreover, the antiferromagnetic interaction anisotropy only weakly suppresses the superconducting gap and density wave amplitude. Our results show that the t-J-U model with hopping anisotropy is qualitatively consistent with experimental superconducting pair symmetry and charge density waves in the YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text] system.

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.

Prevailing Charge Order in Overdoped La_{2-x}Sr_{x}CuO_{4} beyond the Superconducting Dome

The extremely overdoped cuprates are generally considered to be Fermi liquid metals without exotic orders, whereas the underdoped cuprates harbor intertwined states. Contrary to this conventional wisdom, using Cu L_{3}-edge and O K-edge resonant x-ray scattering, we reveal a charge order (CO) correlation in overdoped La_{2-x}Sr_{x}CuO_{4} (0.35≤x≤0.6) beyond the superconducting dome. This CO has a periodicity of ∼6 lattice units with correlation lengths of ∼20 lattice units. It shows similar in-plane momentum and polarization dependence and dispersive excitations as the CO of underdoped cuprates, but its maximum intensity differs along the c direction and persists up to 300 K. This CO correlation cannot be explained by the Fermi surface instability and its origin remains to be understood. Our results suggest that CO is prevailing in the overdoped metallic regime and requires a reassessment of the picture of overdoped cuprates as weakly correlated Fermi liquids.

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.

Monte Carlo study of cuprate superconductors in a four-bandd-pmodel: role of orbital degrees of freedom

Understanding the various competing phases in cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cue_gorbitals and Oporbitals, are a key ingredient for a unified understanding of cuprate superconductors, including the material dependence. Here we investigate a four-bandd-pmodel derived from the first-principles calculations with the variational Monte Carlo method, which allows us to elucidate competing phases on an equal footing. The obtained results can consistently explain the doping dependence of superconductivity, antiferromagnetic and stripe phases, phase separation in the underdoped region, and also novel magnetism in the heavily-overdoped region. The presence ofporbitals is critical to the charge-stripe features, which induce two types of stripe phases withs)-wave andd-wave bond stripe. On the other hand, the presence ofdz2orbital is indispensable to material dependence of the superconducting transition temperature (Tc), and enhances local magnetic moment as a source of novel magnetism in the heavily-overdoped region as well. These findings beyond one-band description could provide a major step toward a full explanation of unconventional normal state and highTcin cuprate supercondutors.

Fate of charge order in overdoped La-based cuprates

In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering study of weak charge correlations in La2-xSrxCuO4 and La1.8-xEu0.2SrxCuO4. Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Long-range temperature-dependent stripe order is only found below optimal doping. At higher doping, short-range temperature-independent correlations are present up to the highest doping measured. This transformation is distinct from and preempts the pseudogap critical doping. We argue that the doping and temperature-independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In La2-xSrxCuO4, long-range static stripe order vanishes around optimal doping and we discuss both quantum critical and crossover scenarios.

Coherent emission from surface Josephson plasmons in striped cuprates

We observe anomalous terahertz emission in photo-excited high-TC cuprates with coexisting superconductivity and charge-stripe order, in absence of any external magnetic field or current bias. Because this phenomenon should be forbidden by symmetry, our observation indicates a symmetry breaking in the stripe phase. The emission spectrum reveals the excitation of surface Josephson plasmons, which are generally dark modes but become coupled to the electromagnetic continuum in these materials by the presence of stripes. The study of coherent anomalous terahertz emission emerges as a sensitive tool to probe the symmetry of superconductors in the presence of frustrated couplings, which is a key topic in the physics of these materials.

The interplay between charge order and superconductivity remains one of the central themes of research in quantum materials. In the case of cuprates, the coupling between striped charge fluctuations and local electromagnetic fields is especially important, as it affects transport properties, coherence, and dimensionality of superconducting correlations. Here, we study the emission of coherent terahertz radiation in single-layer cuprates of the La_2-xBa_xCuO₄ family, for which this effect is expected to be forbidden by symmetry. We find that emission vanishes for compounds in which the stripes are quasi-static but is activated when c-axis inversion symmetry is broken by incommensurate or fluctuating charge stripes, such as in La_1.905Ba_0.095CuO₄ and in La_1.845Ba_0.155CuO₄. In this case, terahertz radiation is emitted by surface Josephson plasmons, which are generally dark modes, but couple to free space electromagnetic radiation because of the stripe modulation.

Pronounced interplay between intrinsic phase-coexistence and octahedral tilt magnitude in hole-doped lanthanum cuprates

Definitive understanding of superconductivity and its interplay with structural symmetry in the hole-doped lanthanum cuprates remains elusive. The suppression of superconductivity around 1/8th doping maintains particular focus, often attributed to charge-density waves (CDWs) ordering in the low-temperature tetragonal (LTT) phase. Central to many investigations into this interplay is the thesis that La_1.875Ba_0.125CuO₄ and particularly La_1.675Eu_0.2Sr_0.125CuO₄ present model systems of purely LTT structure at low temperature. However, combining single-crystal and high-resolution powder X-ray diffraction, we find these to exhibit significant, intrinsic coexistence of LTT and low-temperature orthorhombic domains, typically associated with superconductivity, even at 10 K. Our two-phase models reveal substantially greater tilting of CuO₆ octahedra in the LTT phase, markedly buckling the CuO₂ planes. This would couple significantly to band narrowing, potentially indicating a picture of electronically driven phase segregation, reminiscent of optimally doped manganites. These results call for reassessment of many experiments seeking to elucidate structural and electronic interplay at 1/8 doping.

Pseudogap in underdoped cuprate seen in longitudinal magnetoresistance

We report the results of in-plane magnetotransport study of slightly underdoped cuprate La_1.85Sr_0.15CuO₄(LSCO15) with Ni impurity. Increasing Ni contentycauses a sharp drop in longitudinal magnetoresistance (LMR) in LSCO15 to broaden and move towards higher temperatures. TemperatureTmLMR(y)of this local maximum in LMR coincides with temperatureTdev(y), below which ideal resistivity from the parallel-resistor model deviates from itsT²-dependence. A direct comparison with the hole doping evolution of pseudogap (PG) in La2-xSr_xCuO₄(LSCO), possible through the mobile-carrier concentration extracted from the thermopower measurements, allows to equate both characteristic temperaturesTmLMR≅Tdevwith PG opening temperatureT∗. The rate of PG closing by magnetic field parallel to the CuO₂plane, in measurements up to 9 T, is consistent with spin-paramagnetic effect in this configuration and yields PG closing fieldB_pcclose to the second critical fieldBc2predicted for superconducting gap with the help of Werthamer-Helfand-Hohenberg theory. The field anisotropy ofB_pcsuggests that orbital degrees of freedom also play a role in PG formation.

Unveiling Unequivocal Charge Stripe Order in a Prototypical Cuprate Superconductor

In the cuprates, high-temperature superconductivity, spin-density-wave order, and charge-density-wave (CDW) order are intertwined, and symmetry determination is challenging due to domain formation. We investigated the CDW in the prototypical cuprate La_{1.88}Sr_{0.12}CuO_{4} via x-ray diffraction employing uniaxial pressure as a domain-selective stimulus to establish the unidirectional nature of the CDW unambiguously. A fivefold enhancement of the CDW amplitude is found when homogeneous superconductivity is partially suppressed by magnetic field. This field-induced state provides an ideal search environment for a putative pair-density-wave state.

Generic character of charge and spin density waves in superconducting cuprates

The essential physics of the cuprate high-temperature superconductors have been a central focus of condensed-matter physics for more than three decades. Although initially controversial, it is now clear that a ubiquitous tendency toward charge-density-wave (CDW) order is intertwined with the superconductivity. However, this manifests differently in distinct cuprates. On the basis of extensive X-ray and neutron scattering studies of the temperature and doping dependence of the CDW and spin-density-wave (SDW) correlations in one representative cuprate and a comparison with existing studies on other cuprates, we show that there plausibly is a single, preferred CDW order at the microscale, whose manifestation at low temperatures is modified in predictable ways by material-specific details, including its interaction with SDW order.

Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La1.8−xEu0.2Sr_xCuO₄ over a range of doping 0.07≤x≤0.20. We find that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau–Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in all families of cuprates forms by a common mechanism.

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.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Two-Dimensional Superconducting Fluctuations Associated with Charge-Density-Wave Stripes in La_{1.87}Sr_{0.13}Cu_{0.99}Fe_{0.01}O_{4}

The presence of a small concentration of in-plane Fe dopants in La_{1.87}Sr_{0.13}Cu_{0.99}Fe_{0.01}O_{4} is known to enhance stripelike spin and charge density wave (SDW and CDW) order and suppress the superconducting T_{c}. Here, we show that it also induces highly two-dimensional superconducting correlations that have been argued to be the signatures of a new form of superconducting order, the so-called pair density wave (PDW) order. In addition, using resonant soft x-ray scattering, we find that the two-dimensional superconducting fluctuation is strongly associated with the CDW stripe. In particular, the PDW signature first appears when the correlation length of the CDW stripe grows over eight times the lattice unit (∼8a). These results provide critical conditions for the formation of the PDW order.

Strongly Correlated Charge Density Wave in La_{2-x}Sr_{x}CuO_{4} Evidenced by Doping-Dependent Phonon Anomaly

The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive resonant inelastic x-ray scattering study of La_{2-x}Sr_{x}CuO_{4} finding that charge-density wave effects persist up to a remarkably high doping level of x=0.21 before disappearing at x=0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.