Ruddlesden-Popper nickelates exhibit high-temperature superconductivity closely intertwined with charge and spin density waves. However, fundamental questions persist regarding the interplay between the associated density wave (DW) fluctuations and superconductivity, as well as the orbital character and symmetry underlying the DW instabilities. Here we utilize polarized Raman scattering to investigate the phononic and electronic Raman responses of the trilayer nickelate La_4Ni_3O_10 across its concomitant charge and spin density wave transitions. In addition to distinct phonon anomalies occurring below the transition temperature, we observe a depletion of continuum spectral weight up to 114 meV and a pronounced peak centered at this energy. By combining momentum-selective information from polarized electronic Raman scattering with Raman-response model calculations based on a multiorbital Raman vertex in a reconstructed two-orbital DW state involving both Ni-3d_x^2 - y^2 and Ni-3d_z^2 orbitals, we identify 114 meV as the energy scale 2Δ_DW of the DW gap, characterized by incoherent opening and non-mean-field behavior. Furthermore, the model calculations reveal that the corresponding 2Δ_DW peak has a multiorbital origin, requiring both orbital contributions and their mixing beyond single-orbital projections, thus shedding light on the nature of the DW instabilities in La_4Ni_3O_10.

Layered two-dimensional electron systems exhibit both optical and acousticlike plasmons around the Brillouin-zone center. In the layered cuprate La_2-xSr_xCuO_4, resonant inelastic x-ray scattering (RIXS) has detected corresponding acousticlike plasmons in a low-energy regime comparable to that of other collective excitations associated with distinct regions of the cuprate phase diagram. This overlap in energy scale raises the question of whether the acousticlike plasmons are significantly influenced by phase-specific electronic phenomena, including the pseudogap, charge and spin order, superconductivity, and strange-metal behavior. Here we show that a single parameter set of the layered t-J-V model, which incorporates strong correlations and the long-range Coulomb interaction V, consistently describes the acousticlike plasmon dispersion across all currently available RIXS data from the underdoped to the heavily overdoped regime. This transferability of a single parameter set exceeds that of earlier theoretical descriptions and supports a picture in which strong correlations persist into the heavily overdoped regime, while the collective plasmon mode exhibits only limited sensitivity to the phase-specific electronic phenomena that distinguish different regions of the phase diagram.

The recent discovery of high-temperature superconductivity in both bulk and thin-film bilayer nickelates La 3 Ni 2 O 7 has garnered significant attention. However, the corresponding pairing symmetry remains debated in both experiments and theoretical studies due to conflicting experimental evidence from bulk and thin-film materials. In this work, we examine the electronic Raman response across different channels for various pairing symmetries within a two-orbital bilayer model. By comparing Raman susceptibilities obtained from multiorbital and band-additive approaches, we demonstrate that Raman response can distinguish between different pairing symmetries and identify pocket-dependent gap amplitudes for both fully gapped and nodal superconducting states. Specifically, the nodal d x 2 - y 2 / d xy -wave pairing exhibits robust low-energy power-law behavior, distinct from a fully gapped pairing. Additionally, for the s ± -wave pairing, the detailed gap anisotropy on the β pocket can be determined. Possible experimental implications are also discussed. Our results highlight the crucial role of multiorbital effects in shaping the Raman spectra and establish electronic Raman scattering as a powerful and symmetry-resolved probe for determining the superconducting gap in unconventional superconductors.

Recently plasmon excitations in bilayer lattice systems were studied extensively in the weak-coupling regime. Unlike single-layer systems, these bilayers exhibit two distinct modes, omega f, which show characteristic dependences upon the momentum and hopping integrals along the z direction. To apply them to cuprates, strong correlation effects should be considered, but a comprehensive analysis has not yet been investigated. In this work, we present a strong-coupling theory to analyze the charge dynamics of a bilayer system, utilizing the t-J-V model, which includes the long-range Coulomb interaction, V, on a lattice. Although our theoretical framework is fundamentally different from the weak-coupling approach, we find that resulting plasmon excitations are similar to those of a weak-coupling theory. A key distinction is that our strong-coupling framework reveals a noticeable suppression of particle-hole excitations, which allows the plasmon modes to remain well defined over a wider region of momentum. We suggest that the experimentally reported plasmon excitations in Y-based cuprates can be described by the omega- mode, although we call for more systematic experiments to verify this.

The recent discovery of high-T_c superconductivity in pressurized and thin film nickelates is nowadays one of the most relevant and active topics in solid-state physics. The origin of superconductivity together with the relevance of multiorbital physics are highly discussed issues in this field. Knowledge of the size of the gap and its symmetry is of fundamental interest to uncover the superconducting mechanism at play in the nickelates. Electronic Raman scattering is a powerful tool to investigate the main characteristics of the gap. Here, we investigate the Raman response in the superconducting phase for three different models: Two-orbital models, including d_x^2-y^2 and d_z^2 orbitals, with one and two layers; as well as a bilayer model with the d_x^2-y^2 orbital as the only active one. For each of these models, we consider different pairing symmetries and determine their characteristic fingerprints in the Raman response. For the two-orbital models, we perform full multiorbital calculations including interorbital and intraorbital scattering, and compare the results with those obtained using the additive Raman response where each band is considered separately. Our results should be useful for discussing the minimal model for superconductivity and its pairing symmetry in nickelates. The obtained results and discussions, as well as the presented formalism, are also of general interest for other multiorbital systems.

Almost four decades of intense research have been invested to study the physics of high-Tc cuprate superconductors. The recent discovery of high-Tc superconductivity in pressurized bilayer nickelates and its potential similarities with cuprate superconductors may open a new window to understand this long-standing problem. We have studied the proposed bilayer t-J1I-J1 model [where J1I (J1) is the in-plane (out-of-plane) magnetic exchange] in a large-N approach on the basis of the path integral representation for Hubbard operators, which allows to obtain results at mean-field and beyond mean-field level. We find that J1 is a candidate for triggering high superconducting Tc values at quarter filling (hole doping delta = 0.5) of the dx2-y2 orbitals. Beyond mean-field level, we find a new phase, an out-of-plane bond-order phase (z-BOP), triggered also by J1. z-BOP develops below a critical temperature which decreases with increasing doping and vanishes at a quantum critical point below quarter filling. The occurrence of this phase and its competition with superconductivity leads to a superconducting dome-shaped behavior as a function of doping and as a function of J1. Qualitative comparisons with the physics of cuprates and the recent literature on the new pressurized nickelates are given along the paper.

Within a homologous series of cuprate superconductors, variations in the stacking of CuO2 layers influence the collective charge dynamics through the long-range Coulomb interactions. We use O K-edge resonant inelastic x-ray scattering to reveal plasmon excitations in the optimally doped trilayer Bi2Sr2Ca2Cu3O10+delta. The observed plasmon exhibits nearly qz-independent dispersion and a large excitation gap of approximately 300 meV. This mode is primarily ascribed to the omega- mode, where the charge density on the outer CuO2 sheets oscillates out of phase while the density in the inner sheet remains unaltered at qz = 0. The intensity of the acoustic omega 3 mode is relatively weak and becomes vanishingly small near (qx, qy) = (0, 0). This result highlights a qualitative change in the eigenmode of the dominant low-energy plasmon with the number of CuO2 layers.

Estimating many-body effects that deviate from an independent particle approach has long been a key research interest in condensed matter physics. Layered cuprates are prototypical systems, where electron-electron interactions are found to strongly affect the dynamics of single-particle excitations. It is, however, still unclear how the electron correlations influence charge excitations, such as plasmons, which have been variously treated with either weak or strong correlation models. In this work, we demonstrate the hybridized nature of collective valence charge fluctuations leading to dispersing acoustic-like plasmons in hole-doped La_{1.84}Sr_{0.16}CuO_{4} and electron-doped La_{1.84}Ce_{0.16}CuO_{4} using the two-particle probe, resonant inelastic x-ray scattering. We then describe the plasmon dispersions in both systems, within both the weak-coupling mean-field random phase approximation (RPA) and strong-coupling t-J-V model in a large-N scheme. The t-J-V model, which includes the correlation effects implicitly, accurately describes the plasmon dispersions as resonant excitations outside the single-particle intraband continuum. In comparison, a quantitative description of the plasmon dispersion in the RPA approach is obtained only upon explicit consideration of renormalized electronic band parameters. Our comparative analysis shows that electron correlations significantly impact the low-energy plasmon excitations across the cuprate doping phase diagram, even at long wavelengths. Thus, complementary information on the evolution of electron correlations, influenced by the rich electronic phases in condensed matter systems, can be extracted through the study of two-particle charge response.

Charge excitation spectra are getting clear in cuprate superconductors in momentum -energy space especially around a small momentum region, where plasmon excitations become dominant. Here, we study whether Landau quasiparticles survive in the presence of charge fluctuations observed in experiments. We employ the layered t -J model with the long-range Coulomb interaction, which can reproduce the realistic charge fluctuations. We find that Landau quasiparticles are retained in a realistic temperature and doping region, although the quasiparticle spectral weight is strongly reduced to 0.08-0.24. Counterintuitively, the presence of this small quasiparticle weight does not work favorably to generate a pseudogap.

The essential building blocks of cuprate superconductors are two-dimensional CuO$_2$ sheets interspersed with charge reservoir layers. In bilayer cuprates, two closely spaced CuO$_2$ sheets are separated by a larger distance from the subsequent pair in the next unit cell. In contrast to single-layer cuprates, prior theoretical work on bilayer systems has predicted two distinct acoustic plasmon bands for a given out-of-plane momentum transfer. Here we report random phase approximation (RPA) calculations for bilayer systems which corroborate the existence of two distinct plasmons bands. We find that the intensity of the lower-energy band is negligibly small, whereas the higher-energy band carries significant spectral weight. We also present resonant inelastic x-ray scattering (RIXS) experiments at the O $K$-edge on the bilayer cuprate Y$_{0.85}$Ca$_{0.15}$Ba$_2$Cu$_3$O$_7$ (Ca-YBCO), which show only one dispersive plasmon branch, in agreement with the RPA calculations. In addition, the RPA results indicate that the dispersion of the higher-energy plasmon band in Ca-YBCO is not strictly acoustic, but exhibits a substantial energy gap of approximately 250 meV at the two-dimensional Brillouin zone center.

The discovery of superconductivity in infinite-layer nickelates is presently an important topic in condensed-matter physics, and potential similarities to and differences from cuprates are under intense debate. We determine general features of the charge excitation spectrum in nickelates from two opposite viewpoints: (i) Nickelates are regarded as strongly correlated electron systems like cuprate superconductors and thus can be described by the $t$-$J$ model, and (ii) electron correlation effects are not as strong as in cuprates, and thus, random-phase approximation (RPA) calculations may capture the essential physics. We find that in both cases, plasmon excitations are realized around the momentum transfer $\vq=(0,0,q_z)$, although they tend to be damped more strongly in the RPA. In particular, this damping is enhanced by the relatively large interlayer hopping expected in nickelates. Besides reproducing the optical plasmon at $\vq=(0,0,0)$ observed in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$, we obtain low-energy plasmons with gaps of $\sim 360$ and $\sim 560$ meV at $\vq=(0,0,q_z)$ for finite $q_z$ in cases (i) and (ii), respectively. The present work offers a possible theoretical hint to answer whether nickelates are cupratelike or not and contributes to the general understanding of the charge dynamics in nickelates.

We use resonant inelastic x-ray scattering (RIXS) at the O K- and Cu K-edges to investigate the doping dependence and temperature dependence of low-energy plasmon excitations in La2-xSrxCuO4. We observe a monotonic increase of the energy scale of the plasmons with increasing doping x in the underdoped regime, whereas a saturation occurs above optimal doping x greater than or similar to 0.16 and persists at least up to x = 0.4. Furthermore, we find that the plasmon excitations show only a marginal temperature dependence, and possible effects due to the superconducting transition and the onset of strange metal behavior are either absent or below the detection limit of our experiment. Taking into account the strongly correlated character of the cuprates, we show that layered t -JV model calculations accurately capture the increase of the plasmon energy in the underdoped regime. However, the computed plasmon energy continues to increase even for doping levels above x greater than or similar to 0.16, which is distinct from the experimentally observed saturation and reaches a broad maximum around x = 0.55. We discuss whether possible lattice disorder in overdoped samples, a renormalization of the electronic correlation strength at high dopings, or an increasing relevance of nonplanar Cu and O orbitals could be responsible for the discrepancy between experiment and theory for doping levels above x = 0.16.

Metallic systems exhibit plasmons as elementary charge excitations. This fundamental concept was reinforced also in high-temperature cuprate superconductors recently, although cuprates are not only layered systems but also strongly correlated electron systems. Here, we study how such ubiquitous plasmons leave their marks on the electron dispersion in cuprates. In contrast to phonons and magnetic fluctuations, plasmons do not yield a kink in the electron dispersion. Instead, we find that the optical plasmon accounts for an emergent band -- plasmarons -- in the one-particle excitation spectrum; acoustic-like plasmons typical to a layered system are far less effective. Because of strong electron correlations, the plasmarons are generated by bosonic fluctuations associated with the local constraint, not by the usual charge-density fluctuations. Apart from this physical mechanism, the plasmarons are similar to those discussed in alkali metals, Bi, graphene, monolayer transition-metal dichalcogenides, semiconductors, diamond, two-dimensional electron systems, and SrIrO3 films, establishing a concept of plasmarons in metallic systems in general. Plasmarons are realized below (above) the quasiparticle band in electron-doped (hole-doped) cuprates, including a region around (pi,0) and (0,pi) where the superconducting gap and the pseudogap are most enhanced.

We use resonant inelastic x-ray scattering to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr_{0.9}La_{0.1}CuO_{2}. We detect a plasmon gap of ∼120  meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in Sr_{0.9}La_{0.1}CuO_{2} are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered t-J-V model calculations. A similar analysis performed on recent resonant inelastic x-ray scattering data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interlayer hopping t_{z}. Our work signifies the three dimensionality of the charge dynamics in layered cuprates and provides a new method to determine t_{z}.

The study of the charge excitations in cuprates is presently an interesting topic because of the development of new and precise x-ray experiments. Based on a large -N formulation of the two-dimensional t -J model, which allows us to consider all possible charge excitations on an equal footing, we investigate the charge spectrum for both electron-and hole-doped cases. In both cases, the instability toward phase separation, which has momentum modulation q = (0, 0), is found to be robust in a large region of the doping-temperature phase diagram. If a short-range Coulomb repulsion is included the phase separation region shrinks, but the instability remains at q = (0, 0). If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at q momenta forming a ring around q = (0, 0). The computed charge spectrum in the translation-invariant phase shows well-formed rings. We discuss our results in the light of recent x-ray experiments in electron-and hole-doped cuprates, where ring-like shaped charge modulations have been reported.

The occurrence of retarded (with glue) and unretarded (without glue) pairing is thoroughly discussed in cuprates. We analyze some aspects of this problem in the context of the t-J-V model in a large-N approximation. When 1/N renormalizations are neglected the mean-field result is recovered, where the unretarded d-wave superconducting pairing triggered by the spin-exchange interaction J is obtained. However, the presence of a nonnegligible nearest-neighbors Coulomb interaction V (q) kills superconductivity. If the non-double-occupancy constraint and its fluctuations are considered, the situation changes drastically. In this case, V (q) is screened making d-wave superconductivity very robust. In addition, we show that the early proposal for the presence of an unretarded pairing contribution triggered by the spin-exchange interaction J can be discussed in this context.

Employing a large-N scheme of the layered t-J model with the long-range Coulomb interaction, which captures fine details of the charge excitation spectra recently observed in cuprate superconductors, we explore the role of the charge fluctuations on the electron self-energy. We fix temperature at zero and focus on quantum charge fluctuations. We find a pronounced asymmetry of the imaginary part of the self-energy Im$\Sigma({\bf k}, \omega)$ with respect to $\omega = 0$, which is driven by strong electron correlation effects. The quasiparticle weight is reduced dramatically, which occurs almost isotropically along the Fermi surface. Concomitantly an incoherent band and a sharp side band are newly generated and acquire sizable spectral weight. All these features are driven by usual on-site charge fluctuations, which are realized in a rather high-energy region and yield plasmon excitations. On the other hand, the low-energy region with the scale of the superexchange interaction J is dominated by bond-charge fluctuations. Surprisingly, compared with the effect of the on-site charge fluctuations, their effect on the electron self-energy is much weaker even if the system approaches close to bond-charge instabilities. Furthermore, quantum charge dynamics does not produce a clear kink nor a pseudogap in the electron dispersion.

High T_{c} superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic x-ray scattering to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors (La_{1.84}Sr_{0.16}CuO_{4} and Bi_{2}Sr_{1.6}La_{0.4}CuO_{6+δ}), crucially completing the picture. Interestingly, in contrast to the quasistatic charge ordering which manifests at both Cu and O sites, the observed acoustic plasmons are predominantly associated with the O sites, revealing a unique dichotomy in the behavior of valence charges in hole-doped cuprates.

The external area-to-volume ratio of the ammonite shell has been held to be related to morphology but never evaluated quantitatively. A dimensionless ratio, the Vogel number, was computed for large samples of Devonian to Cretaceous ammonites with a new method based on the ADA-model. The estimated ratios range from 2.4 to 3.4. The highest values are exhibited by uncoiled serpenticone ammonites, lowering in the sequence serpenticone-oxycone-spherocone. It is shown that the area-to-volume relationships are controlled by the involution (degree of overlapping) and the relative width of whorl section. The typical evolutionary trends serpenticone-spherocone and/or serpenticone-oxycone, broadly documented through the history of the Ammonoidea, could have been driven, at least in part, by the lowering of the area-to-volume ratio.

Recently resonant inelastic x-ray scattering experiments reported fine details of the charge excitations around the in-plane momentum ${\bf q}_{\parallel}=(0,0)$ for various doping rates in electron-doped cuprates ${\rm La_{2-x}Ce_xCuO_4}$. We find that those new experimental data are well captured by acoustic-like plasmon excitations in a microscopic study of the layered $t$-$J$ model with the long-range Coulomb interaction. The acoustic-like plasmon is not a usual plasmon typical to the two-dimensional system, but has a small gap proportional to the interlayer hopping $t_z$.