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Almost four decades of intense research have been invested to study the physics of high-T$_c$ cuprate superconductors. The recent discovery of high-T$_c$ superconductivity in pressurized bilayer nickelates and its potential similarities with cuprate superconductors may open a new window to understand this long standing problem. Motivated by this we have assumed that nickelates belong to the category of strongly correlated systems, and considered the bilayer $t$-$J_\parallel$-$J_\perp$ model as a minimal model, where $J_\parallel$ and $J_\perp$ are the in-plane and out-of-plane magnetic exchange, respectively. We have studied the $t$-$J_\parallel$-$J_\perp$ model 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 $J_\perp$ is a promising candidate for triggering high superconducting $T_c$ values at quarter filling (hole doping $\delta=0.5$) of the $d_{x^2-y^2}$ orbitals. Beyond mean-field level, we remarkably find a new phase, an out-of-plane bond-order phase (z-BOP), triggered also by $J_\perp$. 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 $J_\perp$. Comparisons with the physics of cuprates and the recent literature on the new pressurized nickelates are given along the paper., Comment: 7 pages (main text) + 8 pages (references + appendices), 7 figures

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 hybridised 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 mean-field Random Phase Approximation (RPA) and strong coupling $t$-$J$-$V$ models. The $t$-$J$-$V$ model, which includes the correlation effects implicitly, accurately describes the plasmon dispersions as resonant excitations outside the single-particle intra-band continuum. In comparison, a quantitative description of the plasmon dispersion in the RPA approach is obtained only upon explicit consideration of re-normalized 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., Comment: 6 Figures

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., Comment: 21 pages, 7 figures

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 ${\bf q}=(0,0)$, 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 ${\bf q}=(0,0)$. If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at ${\bf q}$ momenta forming a ring around ${\bf q}=(0,0)$. 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., Comment: 21 pages, 8 figures

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., Comment: 27 pages, 9 figures

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., Comment: 21 pages, 5 figures

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 non-negligible 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., Comment: 19 pages, 3 figures

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., Comment: 49 pages, 17 figures

High Tc 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 (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing the picture. Interestingly, in contrast to the quasi-static 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 behaviour of valence charges in hole-doped cuprates., Comment: 11 pages, 7 figures + Supplementary Information

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 $t_z$., Comment: 14 pages, 4 figures

We study the occurrence and the origin of ferromagnetic fluctuations in the longitudinal spin susceptibility of the $t$-$t'$-Rashba-Hubbard model on the square lattice. The combined effect of the second-neighbor hopping $t'$ and the spin-orbit coupling leads to ferromagnetic fluctuations in a broad filling region. The spin-orbit coupling splits the energy bands, leading to two van Hove fillings, where the sheets of the Fermi surface change their topology. Between these two van Hove fillings the model shows ferromagnetic fluctuations. We find that these ferromagnetic fluctuations originate from interband contributions to the spin susceptibility. These interband contributions only arise if there is one holelike and one electronlike Fermi surface, which is the case for fillings in between the two van Hove fillings. We discuss implications for experimental systems and propose a test on how to identify these types of ferromagnetic fluctuations in experiments., Comment: 7 pages, 5 figures

The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-plane momentum (0,0) captures the major features of the high-energy charge excitations. The high-energy charge excitations, therefore, should be a universal feature in cuprate superconductors and are expected also in the hole-doped cuprates. Acoustic-like plasmons in cuprates have not been recognized yet in experiments. We propose several experimental tests to distinguish different interpretations of the high-energy charge excitations., Comment: 19 pages, 5 figures; Supplemental material included; to appear in Communications Physics

Motivated by the recent experiments reporting the doping dependence of the short-range charge order (CO) in electron-doped cuprates, we study the resonant x-ray scattering spectrum from d-wave bond-charge fluctuations obtained in the two-dimensional t-J model. We find that (i) the CO is short-range, (ii) the CO peak is pronounced at low temperature, (iii) the peak intensity increases with decreasing carrier doping $\delta$ down to $\delta \approx$ 0.10 and is substantially suppressed below $\delta \approx$ 0.10 due to strong damping, and (iv) the momentum of the CO decreases monotonically down to $\delta \approx$ 0.10 and goes up below $\delta \approx$ 0.10. These results reasonably capture the major features of the experimental data, and the observed short-range CO can be consistently explained in terms of bond-charge fluctuations with an internal d-wave symmetry., Comment: 19 pages, 6 figures; some sections rewritten, appendix added, author name corrected; minor changes

Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments in electron-doped cuprates, we study the charge excitation spectrum in a layered t-J model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (J-term) whereas high-energy charge excitations are due to usual on-site charge fluctuations and correspond to plasmon excitations above the particle-hole continuum. The interlayer coupling, which is frequently neglected in many theoretical studies, is particularly important to the high-energy charge excitations., Comment: 28 pages, 9 figures; [v3] slight change in title to match published version

We study the density-density correlation function in a large-N scheme of the t-t'-J-V model. When the nearest-neighbor Coulomb interaction V is zero, our model exhibits phase separation in a wide doping region and we obtain large spectral weight near momentum q=(0,0) at low energy, which originates from the proximity to phase separation. These features are much stronger for electron doping than for hole doping. However, once phase separation is suppressed by including a finite V, the low-energy spectral weight around q=(0,0) is substantially suppressed. Instead a sharp zero-sound mode is stabilized above the particle-hole continuum. We discuss that the presence of a moderate value of V, which is frequently neglected in the t-J model, is important to understand low-energy charge excitations especially close to q=(0,0) for electron doping. This insight should be taken into account in a future study of x-ray scattering measurements., Comment: 12 pages, 3 figures

Motivated by the recent resonant inelastic x-ray scattering (RIXS) experiment for the electron-doped cuprates Nd_{2-x}Ce_{x}CuO_{4} with x around 0.15, we compute the density-density correlation function in the t-J model on a square lattice by including interlayer hopping and the long-range Coulomb interaction. We find that collective charge excitations are realized not inside the particle-hole continuum, but above the continuum as plasmons. The plasmon mode has a rather flat dispersion near the in-plane momentum q=(0,0) with a typical excitation energy of the order of the intralayer hopping t when the out-of-plane momentum qz is zero. However, when qz becomes finite, the plasmon dispersion changes drastically near q=(0,0), leading to a strong dispersive feature with an excitation gap scaled by the interlayer hopping tz. We discuss that the mode recently observed by RIXS near q=(0,0) can be associated with the plasmon mode with a finite qz., Comment: 19 pages, 7 figures; Authors names corrected in arXiv's metadata; Added one figure

We study charge excitation spectra in the two-dimensional $t$-$J$ model on a square lattice to explore a charge-order tendency recently found in electron-doped cuprates around the carrier density 0.15. The static susceptibility of $d$-wave charge density, which corresponds to the nematic susceptibility at the momentum transfer ${\bf q}=(0,0)$, shows two characteristic peaks at momenta of the form ${\bf q}_{1}=(q',q')$ and ${\bf q}_{2}=(q,0)$. These two peaks originate from the so-called $2k_{F}$ scattering processes enhanced by the $d$-wave character of the bond-charge density. The peak at ${\bf q}_{1}$ is much broader, but develop to be very sharp in the vicinity of its instability, whereas the peak at ${\bf q}_{2}$ becomes sharper with decreasing temperature, but does not diverge. The equal-time correlation function, which is measured by resonant x-ray scattering, exhibits a momentum dependence similar to the static susceptibility. We also present energy-resolved charge excitation spectra. The spectra show a V-shaped structure around ${\bf q}=(0,0)$ and bend back toward close to zero energy due to the charge-order tendency at ${\bf q}_{1}$ and ${\bf q}_{2}$. The resulting spectra form gap-like features with a maximal gap at ${\bf q} \approx {\bf q}_{1}/2$ and ${\bf q}_{2}/2$. We discuss implications for the recent experiments in electron-doped cuprates., Comment: 6 pages, 4 figures, panel b of figure 1 corrected, added references, corrected typos, added a paragraph before summary

One of the puzzling characteristics of the pseudogap phase of high-$T_c$ cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an associated pseudogap. Angle-resolved photoemission spectroscopy and electronic Raman scattering are two valuable tools which have shown universal features which are rather material-independent, and presumably intrinsic to the pseudogap phase. The doping and temperature dependence of the Fermi arcs and the pseudogap observed by photoemission near the antinode correlates with the non-Fermi liquid behaviour observed by Raman for the B$_{1g}$ mode. In contrast, and similar to the nodal quasiparticles detected by photoemission, the Raman B$_{2g}$ mode shows Fermi liquid features. We show that these two experiments can be analysed, in the context of the $t$-$J$ model, by self-energy effects in the proximity to a d-wave flux-phase order instability. This approach supports a crossover origin for the pseudogap, and a scenario of two competing phases. The B$_{2g}$ mode shows, in an underdoped case, a depletion at intermediate energy which has attracted a renewed interest. We study this depletion and discuss its origin and relation with the pseudogap., Comment: 12 pages, 6 figures

We study possible charge instabilities in doped Mott insulators by employing the two-dimensional t-J model with a positive value of the next nearest-neighbor hopping integral t' on a square lattice, which is applicable to electron-doped cuprates. Although the d-wave charge density wave (flux phase) and d-wave Pomeranchuk instability (nematic order) are dominant instabilities for a negative t' that corresponds to hole-doped cuprates, we find that those instabilities are strongly suppressed and become relevant only rather close to half filling. Instead, various types of bond orders with modulation vectors close to (pi,pi) are dominant in a moderate doping region. Phase separation is also enhanced, but it can be suppressed substantially by the nearest-neighbor Coulomb repulsion without affecting the aforementioned charge instabilities., Comment: 16 pages, 7 figures

Hole doped cuprates show a superconducting critical temperature $T_c$ which follows an universal dome-shaped behavior as function of doping. It is believed that the origin of superconductivity in cuprates is entangled with the physics of the pseudogap phase. An open discussion is whether the source of superconductivity is the same that causes the pseudogap properties. The $t$-$J$ model treated in large-N expansion shows $d$-wave superconductivity triggered by non-retarded interactions, and an instability of the paramagnetic state to a flux phase or $d$-wave charge density wave ($d$-CDW) state. In this paper we show that self-energy effects near $d$-CDW instability may lead to a dome-shaped behavior of $T_c$. In addition, it is also shown that these self-energy contributions may describe several properties observed in the pseudogap phase. In this picture, although fluctuations responsible for the pseudogap properties leads to a dome-shaped behavior, they are not involved in pairing which is mainly non-retarded., Comment: 11 pages, 7 figures, accepted for publication in Phys. Rev. B

Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-N expansion formulated in a path integral representation of the two-dimensional t-J model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the 1/N expansion. While the d-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a d-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling., Comment: 28 pages, 6 figures

The pseudogap phase of high-$T_c$ cuprates is controversially attributed to preformed pairs or to a phase which coexists and competes with superconductivity. One of the challenges is to develop theoretical and experimental studies in order to distinguish between both proposals. Very recently, researchers at Stanford have reported [M. Hashimoto {\it et al.}, Nat. Phys. {\bf 6}, 414 (2010); R.-H. He {\it et al.}, Science {\bf 331}, 1579 (2011)] angle-resolved photoemission spectroscopy experiments on Pb-Bi2201 supporting the point of view that the pseudogap is distinct from superconductivity and associated to a spacial symmetry breaking without long-range order. In this paper we show that many features reported by these experiments can be described in the framework of the t-J model considering self-energy effects in the proximity to a d charge-density-wave instability., Comment: 4.1 pages, 6 figures

At mean-field level the t-J model shows a phase diagram with close analogies to the phase diagram of hole doped cuprates. An order parameter associated with the flux or $d$ charge-density wave ($d$-CDW) phase competes and coexists with superconductivity at low doping showing characteristics identified with the observed pseudogap in underdoped cuprates. In addition, in the $d$-CDW state the Fermi surface is reconstructed toward pockets with low spectral weight in the outer part, resembling the arcs observed in angle-resolved photoemission spectroscopy experiments. However, the $d$-CDW requires broken translational symmetry, a fact that is not completely accepted. Including self-energy corrections beyond the mean, field we found that the self-energy can be written as two distinct contributions. One of these (called $\Sigma_{flux}$) dominates at low energy and originates from the scattering between carriers and $d$-CDW fluctuations in proximity to the $d$-CDW instability. The second contribution (called $\Sigma_{R\lambda}$) dominates at large energy and originates from the scattering between charge fluctuations under the constraint of non double occupancy. In this paper it is shown that $\Sigma_{flux}$ is responsible for the origin of low-energy features in the spectral function as a pseudogap and Fermi arcs. The obtained doping and temperature dependence of the pseudogap and Fermi arcs is similar to that observed in experiments. At low energy, $\Sigma_{R \lambda}$ gives an additional contribution to the closure of the pseudogap., Comment: 11 pages, 13 figures