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We perform a comprehensive study of charge excitations in a bilayer electron system in the presence of the long-range Coulomb interaction (LRC). Our major point is to derive formulae of the LRC that fully respect the bilayer lattice structure. This is an extension of the LRC obtained by Fetter in the electron-gas model 50 years ago and can now be applicable to any electron density. We then provide general formulae of the charge susceptibility in the random phase approximation and study them numerically. The charge ordering tendency is not found and instead we find two plasmon modes, w_{+} and w_{-} modes. Our second major point is to elucidate their spectral weight distribution and the effect of electron tunneling between the layers. The spectral weight of the w_{+-} modes does not have 2pi periodicity along the q_{z}c direction. The w_{+} mode loses spectral weight at inplane momentum q_{||}=(0,0) at q_{z}c=2n pi with n being integer whereas the w_{-} mode has no spectral weight at q_{z}c=0 for any q_{||} but acquires sizable spectral weight at q_{z}c=2n pi with n \ne 0. Both w_{+-} modes are gapped at q_{||}=(0,0). When q_{z}c is away from 2n pi, the w_{+-} modes show striking behavior. When the intrabilayer hopping t_z is relatively small (large), the w_{-} (w_{+}) mode becomes gapless at q_{||}=(0,0) whereas the w_{+} (w_{-}) mode retains the gap. However, when the interbilayer hopping integral t_{z}' is taken into account, the gapless mode acquires a gap at q_{||}=(0,0) and both w_{+-} modes are gapped at any q_{z}c. To highlight the special feature of the LRC, we also clarify a difference to the case of a short-range interaction. While the strong electron correlation effects are not included, the present theory captures available data of the charge excitations observed by resonant inelastic x-ray scattering for Y-based cuprate superconductors., Comment: 43 pages, 18 figures

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector $\vec{Q}= \vec{0}$. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian momentum-shell renormalization group (RG) theory capturing the infrared scaling should be formulated keeping $\vec{Q}$ as a flowing, scale-dependent quantity. At the quantum critical point, scaling controlled by the dynamical exponent $z=3$ is overshadowed by a broad scaling regime characterized by a lower value of $z \approx 2$. This in particular offers an explanation of the results of quantum Monte Carlo simulations pertinent to the electronic nematic quantum critical point.

Magnetic and bond-charge interactions can arise from the same microscopic interaction. Motivated by this observation, we compute magnetic and bond-charge excitation spectra on an equal footing by introducing a simple effective model on a square lattice, which describes antiferromagnetic and d-wave superconducting phases around half-filling on the electron-doped side. The magnetic excitation spectrum Im chi(q, omega) has strong weight around q=(pi, pi) in low energy and its intensity map exhibits a pencil-tip-like shape in q-omega space. Around q=(0,0) magnetic excitations show a steep dispersion toward the (pi, pi) and (pi,0) directions, which is very similar to a spin-wave dispersion although the system is non-magnetic. Bond-charge excitations are characterized by four different symmetries and studied for all possible couplings. Bond-charge fluctuations with three different symmetries have large spectral weight around q=(pi, pi) in a relatively low-energy region and extend widely more than the magnetic excitation spectrum. The d-wave symmetry of bond-charge excitations also has sizable spectral weight along the direction (pi/2, pi/2)-(0, 0)-(pi/2, 0) in a low-energy region and exhibits softening around q approx (0.5 pi, 0), whereas no such softening is present in the other symmetries. These results capture the essential features observed in electron-doped cuprates and may motivate an experimental test of bond-charge excitations around q=(pi, pi) on top of the strong magnetic excitations there as well as additional softening in the d-wave channel in the (pi, pi)-(pi/2, pi/2) region at low temperatures near the magnetic phase. We extend the present analysis to the hole-doped side and highlight a contrast to the electron-doped side, which includes incommensurate correlations, electronic nematic correlations, and spin and bond-charge resonance modes in the superconducting state., Comment: 59 pages, 29 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

Antiferromagnetic fluctuations are believed to be a promising glue to drive high-temperature superconductivity especially in cuprates. Here, we perform a close inspection of the superconducting mechanism from spin fluctuations in the Eliashberg framework by employing a typical one-band model on a square lattice. While spin fluctuations can eventually drive superconductivity as is well established, we find that the superconducting tendency is suppressed substantially by a seemingly negligible contribution from a small momentum transfer far away from (pi,pi). This suppression comes from phase frustration of the pairing gap and is expected to be a general feature due to the repulsive pairing interaction of spin fluctuations. Furthermore, we find that the momentum dependence of the pairing gap largely deviates from the functional form of cos kx - cos ky, although this form is well established in cuprate superconductors. We argue that an instantaneous magnetic interaction plays the important role to understand high-critical temperature of superconductivity as well as the momentum dependence of the pairing gap., Comment: 28 pages, 11 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

We perform a microscopic study of itinerant ferromagnetic systems. We reveal a very rich phase diagram in the three-dimensional space spanned by the chemical potential, a magnetic field, and temperature beyond the Landau theory analyzed so far. Besides a generic wing structure near a tricritical point upon introducing the magnetic field, we find that an additional wing can be generated close to a quantum critical end point (QCEP) and also even from deeply inside the ferromagnetic phase. A tilting of the wing controls the entropy jump associated with the metamagnetic transition. Ferromagnetic and metamagnetic transitions are usually accompanied by a Lifshitz transition at low temperatures, i.e., a change of Fermi surface topology including the disappearance of the Fermi surface. In particular, the Fermi surface of either spin band vanishes at the QCEP. These rich phase diagrams are understood in terms of the density of states and the breaking of particle-hole symmetry in the presence of a next nearest-neighbor-hopping integral t', which is expected in actual materials. The obtained phase diagrams are discussed in a possible connection to itinerant ferromagnetic systems such as UGe2, UCoAl, ZrZn2, and others including materials exhibiting the magnetocaloric effect., Comment: 25 page, 11 figures

We propose that cuprate superconductors are in the vicinity of a spontaneous d-wave type Fermi surface symmetry breaking, often called a d-wave Pomeranchuk instability. This idea is explored by means of a comprehensive study of magnetic excitations within the slave-boson mean-field theory of the t-J model. We can naturally understand the pronounced xy anisotropy of magnetic excitations in untwinned YBa_{2}Cu_{3}O_{y} and the sizable change of incommensurability of magnetic excitations at the transition temperature to the low-temperature tetragonal lattice structure in La_{2-x}Ba_{x}CuO_{4}. In addition, the present theoretical framework allows the understanding of the similarities and differences of magnetic excitations in Y-based and La-based cuprates., Comment: 10 pages, 3 figures, for those who cannot download J. Phys. Chem. Solids papers

In this article, we focus on the charge degree of freedom in cuprate superconductors and review theoretical insights into the electronic nematic order, bond-charge orders, and plasmons. The low-energy charge dynamics is controlled by the spin-spin interaction J, which generates various bond-charge ordering tendencies including the electronic nematic order. The nematic order is driven by a d-wave Pomeranchuk instability and is pronounced in the underdoped region as well as around van Hove filling in the hole-doped case; the nematic tendency is weak in the electron-doped region. Nematicity consistent with the d-wave Pomeranchuk instability was reported for hole-doped cuprates in various experiments. Although the t-J and Hubbard models correctly predicted the proximity to the nematic instability in cuprates far before the experimental indications were obtained, full understanding of the charge ordering tendencies in hole-doped cuprates still requires further theoretical studies. In electron-doped cuprates, on the other hand, the d-wave bond-charge excitations around momentum q=(0.5pi,0) explain the resonant x-ray scattering data very well. Plasmon excitations are also present and the agreement between the large-N theory of the t-J model and resonant inelastic x-ray scattering measurements is nearly quantitative in both hole- and electron-doped cuprates. Theoretically the charge dynamics in cuprates is summarized as a dual structure in energy space: the low-energy region scaled by J, where the nematic and various bond-charge orders are relevant, and the high-energy region typically larger than J, where plasmons are predominant., Comment: 38 pages, 14 figures, concise review article

To reconcile the two experimental findings on La_{2-x}Sr_{x}CuO_4, namely, Fermi surface (FS) observed by angle-resolved photoemission spectroscopy and sharp incommensurate magnetic peaks by neutron scattering, we propose a picture that a quasi-one-dimensional FS (q-1dFS) is realized in each CuO_{2} plane whose q-1d direction alternates along the c-axis., Comment: 10 pages, 6 figures, for those who cannot download JPSJ papers

On the basis of the picture of a quasi-one-dimensional (q-1d) Fermi surface (FS), recently proposed by authors for LSCO systems, spin excitation spectrum, Im chi(q,omega), is calculated in the 'RPA' within the slave-boson mean-field approximation to the t-J model. It is found that Im chi(q,omega) shows both incommensurate (IC) and diagonal IC (DIC) peaks, whose realization does not depend on the existence of the d-wave gap. The peak positions do not change appreciably with omega and the sharp peaks survive down to the low hole doping rate. The d-wave gap suppresses both the IC peak and the DIC peak, but the degree of suppression as a function of omega is different between them. Taking these results together with results for the two-dimensional FS, we argue that essential features of magnetic excitation in LSCO systems can be understood in terms of the q-1d picture of the FS., Comment: 31 pages, 17 pages, for those who cannot download JPSJ papers

We show within the slave-boson mean field approximation that the two-dimensional t-J model has an intrinsic instability toward forming a quasi-one-dimensional (q-1d) Fermi surface. This q-1d state competes with, and is overcome by, the d-wave pairing state for a realistic parameter choice. However, we find that a small spatial anisotropy in t and J exposes the q-1d instability which has been hidden behind the d-wave pairing state, and brings about the coexistence with the d-wave pairing. We argue that this coexistence can be realized in La_{2-x}Sr_{x}CuO_4 systems, Comment: 15 pages, 10 figures, for those who cannot download JPSJ papers

Compton scattering provides invaluable information on the underlying Fermi surface (FS) and is a powerful tool complementary to angle-resolved photoemission spectroscopy and quantum oscillation measurements. Here we perform high-resolution Compton scattering measurements for La_{2-x}Sr_{x}CuO_{4} with x=0.08 (Tc=20K) at 300K and 150K, and image the momentum distribution function in the two-dimensional Brillouin zone. We find that the observed images cannot be reconciled with the conventional hole-like FS believed so far. Instead, our data imply that the FS is strongly deformed by the underlying nematicity in each CuO_2 plane, but the bulk FSs recover the fourfold symmetry. We also find an unusually strong temperature dependence of the momentum distribution function, which may originate from the pseudogap formation in the presence of the reconstructed FSs due to the underlying nematicity. Additional measurements for x=0.15 and 0.30 at 300K suggest similar FS deformation with weaker nematicity, which nearly vanishes at x=0.30., Comment: 36 pages, 19 figures

We study the longitudinal spin susceptibility inside a magnetically ordered phase, which exhibits a superconducting instability leading to a coexistence of the two ordered phases. Inside the magnetic phase, the superconducting gap acquires a linear term in a magnetic field applied along the direction of the magnetic moment. We find that such a linear term generates a jump of the longitudinal spin susceptibility when the superconducting instability occurs via a continuous phase transition. This anomaly at the superconducting instability is a thermodynamic signature of the microscopic coexistence of superconductivity and magnetism, and can be a general feature associated with the breaking of spin rotational symmetry inside the magnetic phase., Comment: 20 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

We report resistance and elastoresistance measurements on (Ba$_{0.5}$K$_{0.5}$)Fe$_2$As$_2$, CaKFe$_4$As$_4$, and KCa$_2$Fe$_4$As$_4$F$_2$. The Fe-site symmetry is $D_{2d}$ in the first compound but $C_{2v}$ in the latter two, which lifts the degeneracy of the Fe $d_{xz}$ and $d_{yz}$ orbitals. The temperature dependence of the resistance and elastoresistance is similar between the three compounds. Especially, the [110] elastoresistance is enhanced with decreasing temperature irrespective of the Fe-site symmetry. This appears to be in conflict with recent Raman scattering studies on CaKFe$_4$As$_4$, which suggest the absence of nematic fluctuations. We consider possible ways of reconciliation and suggest that the present result is important in elucidating the origin of in-plane resistivity anisotropy in iron-based superconductors., Comment: 8 pages, 5 figures, 1 table

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 superconducting instability mediated by spin fluctuations in the Eliashberg theory for a minimal two-band model of iron-based superconductors. While antiferromagnetic spin fluctuations can drive superconductivity (SC) as is well established, we find that spin fluctuations necessarily contain a contribution to suppress SC even though SC can eventually occur at lower temperatures. This self-restraint effect stems from a general feature of the spin-fluctuation mechanism, namely the repulsive pairing interaction, which leads to phase frustration of the pairing gap and consequently the suppression of SC., Comment: 13 pages, 5 figures

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness., Comment: 13 pages, 3 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 report that special care is needed when longitudinal magnetic susceptibility is computed in a magnetically ordered phase, especially in metals. We demonstrate this by studying static susceptibility in both a ferromagnetic and an antiferromagnetic state in the random phase approximation to the two-dimensional Hubbard model on a square lattice. In contrast to the case in the disordered phase, a first derivative of the chemical potential (or the density) with respect to a magnetic field does not vanish in a magnetically ordered phase when the field is applied parallel to the magnetic moment. This effect is crucial and should be included when computing magnetic susceptibility in the ordered phase, otherwise an unphysical result would be obtained. In addition, consequently the magnetic susceptibility becomes different when computed at a fixed density and a fixed chemical potential in the ordered phase. In particular, we cannot employ magnetic susceptibility at a fixed chemical potential to describe a system with a fixed density even if the chemical potential is tuned to reproduce the correct density., Comment: 19 pages, 8 figures

We study superconducting instability from orbital nematic fluctuations in a minimal model consisting of the $d_{xz}$ and $d_{yz}$ orbitals, and choose model parameters which capture the typical Fermi surface geometry observed in iron-based superconductors. We solve the Eliashberg equations down to low temperatures with keeping the renormalization function and a full momentum dependence of the pairing gap. When superconductivity occurs in the tetragonal phase, we find that the pairing gap exhibits a weak momentum dependence over the Fermi surfaces. The superconducting instability occurs also inside the nematic phase. When the $d_{xz}$ orbital is occupied more than the $d_{yz}$ orbital in the nematic phase, a larger (smaller) gap is realized on the Fermi-surface parts, where the $d_{xz}$ ($d_{yz}$) orbital component is dominant, leading to a substantial momentum dependence of the pairing gap on the hole Fermi surfaces. On the other hand, the momentum dependence of the gap is weak on the electron Fermi surfaces. We also find that while the leading instability is the so-called $s_{++}$-wave symmetry, the second leading one is $d_{x^2-y^2}$-wave symmetry. In particular, these two states are nearly degenerate in the tetragonal phase whereas such quasi-degeneracy is lifted in the nematic phase and the $d_{x^2-y^2}$-wave symmetry changes to highly anisotropic $s$-wave symmetry., Comment: 19 pages, 8 figures

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

We show that a Fermi surface reconstruction due to spiral antiferromagnetic order may explain the rapid change in the Hall number as recently observed near optimal doping in cuprate superconductors [Badoux~\textit{et. al.}, Nature \textbf{531}, 210 (2016)]. The single-particle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight. Adding charge-density wave order further reduces the Fermi surface to a single electron pocket. We propose quantum oscillation measurements to distinguish between commensurate and spiral antiferromagnetic order. Similar results apply to certain metals in which topological order replaces antiferromagnetic order., Comment: 6 pages, 4 figures, including 2 pages supplementary material

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 analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order., Comment: 6 pages, 3 figures, and Supplemental Material

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

We study an interacting electronic system exhibiting a spin nematic instability. Using a phenomenological form for the spin fluctuation spectrum near the spin-density-wave (SDW) phase, we compute the spin nematic susceptibility in energy and momentum space as a function of temperature and the magnetic correlation length xi. The spin nematic instability occurs when xi reaches a critical value xi_{cr}, i.e., its transition temperature T_{SN} is always higher than the SDW critical temperature T_{SDW}. In particular, xi_{cr} decreases monotonically with increasing T_{SN}. Concomitantly, low-energy nematic fluctuations are present in a wider temperature region as T_{SN} becomes higher. Approaching the spin nematic instability, the nematic spectral function at zero momentum exhibits a central peak as a function of energy for a finite temperature and a soft mode at zero temperature. These properties originate from the general feature that the imaginary part of the spin-fluctuation bubble has a term linear in energy and its coefficient is proportional to the square of temperature. Furthermore we find that the nematic spectral function exhibits a diffusive peak around zero momentum and zero energy without clear dispersive features. A possible phase diagram for the spin nematic and SDW transitions is also discussed., Comment: 18 pages, 9 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

We study the phase diagram of electronic nematic instability in the presence of xy anisotropy. While a second order transition cannot occur in this case, mean-field theory predicts that a first order transition occurs near van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing, referring to his original work of He3-He4 mixtures. When crossing the wing, the anisotropy of the electronic system exhibits a discontinuous change, leading to a meta-nematic transition, i.e., the analog to a meta-magnetic transition in a magnetic system. The upper edge of the wing corresponds to a critical end line, which shows a non-monotonic temperature dependence as a function of the external anisotropy and vanishes at a quantum critical end point for a strong anisotropy. The mean-field phase diagram is, however, very sensitive to fluctuations of the nematic order parameter, yielding a topologically different phase diagram. The Griffiths wing is broken into two pieces. A tiny wing appears close to zero anisotropy and the other is realized for a strong anisotropy. Consequently three quantum critical end points are realized. We discuss that these results can be related to various materials including a cold atom system., Comment: 19 pages, 2 figures

We compute Raman scattering intensities via the lowest-order coupling to the bosonic propagator associated with orbital nematic fluctuations in a minimal model for iron pnictides. The model consists of two bands on a square lattice exhibiting four Fermi pockets and a transition from the normal to a nematic state. It is shown that the orbital fluctuations produce in the B1g channel strong quasi-elastic light scattering around the nematic critical temperature Tn, both above and below Tn. This holds for the A1g symmetry only below Tn whereas no low-energy scattering from orbital fluctuations is found in the B2g symmetry. Due to the nematic distortion the electron pocket at the X-point may disappear at low temperatures. Such a Lifshitz transition causes in the B2g spectrum a large upward shift of spectral weight in the high energy region whereas no effect is seen in the other symmetries., Comment: 23 pages, 7 figures

Recent experiments suggest that besides of antiferromagnetic fluctuations nematic fluctuations may contribute to the occurrence of superconductivity in iron pnictides. Motivated by this observation we study superconductivity from nematic fluctuations in a minimal two-band model. The employed band parameters are appropriate for iron pnictides and lead to four pockets for the Fermi line. It is shown that low-energy, long-wavelength nematic fluctuations within the pockets give rise to strong-coupling superconductivity whereas the large momenta density fluctuations between pockets are rather irrelevant. The obtained transition temperatures are similar to those typically found in the pnictides and are rather robust against repulsive Coulomb interactions. The superconducting and nematic states coexist in a large region of the phase diagram., Comment: 5 pages, 4 figures

We analyze an effective model on a square lattice with two types of forward scattering interactions, which, respectively, drive ferromagnetism (FM) and electronic nematic order via a d-wave Pomeranchuk instability (dPI). The FM and dPI in general compete with each other and they are typically separated by a first order phase boundary in the plane of the chemical potential and temperature. Nevertheless there is a parameter region where the dPI occurs inside the FM phase, leading to their coexistence. We also study the effect of a magnetic field by choosing a chemical potential where the ground state is paramagnetic without a field. In this case, instead of FM, the dPI competes with a metamagnetic instability. The latter occurs above a threshold strength of the FM interaction and otherwise the dPI is stabilized with a dome-shaped phase diagram in the plane of a magnetic field and temperature. The FM interaction shifts the center of the dome to a lower field, accompanied by a substantial reduction of the field range where the dPI is stabilized and by an extension of the first order part of the transition line, although the maximal critical temperature does not change. The experimental phase diagram of the bilayer ruthenate Sr3Ru2O7 can be well captured by the present theory., Comment: 22 pages, 8 figures

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

We analyze how thermal fluctuations near a finite temperature nematic phase transition affect the spectral function $A({\bf k},\omega)$ for single-electron excitations in a two-dimensional metal. Perturbation theory yields a splitting of the quasi-particle peak with a d-wave form factor, reminiscent of a pseudogap. We present a resummation of contributions to all orders in the Gaussian fluctuation regime. Instead of a splitting, the resulting spectral function exhibits a pronounced broadening of the quasi-particle peak, which varies strongly around the Fermi surface and vanishes upon approaching the Brillouin zone diagonal. The Fermi surface obtained from a Brillouin zone plot of $A({\bf k},0)$ seems truncated to Fermi arcs., Comment: 5 pages, 3 figures, final version as published

Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity., Comment: 12 pages, 3 figures

We consider a two-dimensional interacting Fermi system which displays a nematic phase within mean-field theory. The system is analyzed using a non-perturbative renormalization-group scheme. We find that order-parameter fluctuations can suppress the nematic order obtained in mean-field theory even at zero temperature. For a suitable choice of parameters a quantum critical point surrounded by a disordered phase can be realized, giving rise to quantum critical behavior in the absence of an ordered regime in the phase diagram., Comment: 8 pages, 3 figures

Motivated by recent transport and neutron scattering experiments suggesting an orientational symmetry breaking in underdoped cuprates we present a theoretical study of Raman scattering near a d-wave Pomeranchuk instability (PI). The d-wave component of Raman scattering from electrons and phonons allows to study directly order parameter fluctuations associated with the PI. Approaching the PI from the normal state by lowering the temperature a central peak emerges both in electronic and, as an additional low-frequency feature, in phononic scattering. Approaching the PI in the superconducting state at low temperature by decreasing the doping concentration the central peak is replaced by a soft mode with strongly decreasing width and energy and increasing spectral weight. These predicted low-energy features in Raman scattering could confirm in a rather direct way the presence of a PI in high-temperature cuprate superconductors and in Sr3Ru2O7., Comment: 26 pages, 9 figures

We study magnetic susceptibilities of two-dimensional itinerant electron systems exhibiting symmetry-breaking Fermi surface distortions, the so-called d-wave Pomeranchuk instability, in a magnetic field. In a pure forward scattering model, the longitudinal susceptibility chi^{zz} is found to exhibit a jump at a critical point. The magnitude of this jump diverges at a tricritical point. When scattering processes involving finite momentum transfers are allowed for, chi^{zz} is expected to diverge also at a critical point. The system displays multiple critical fluctuations. We argue that the features of chi^{zz} are general properties associated with singularities of a non-ordering susceptibility, leading to implications for a variety of materials including Sr_3Ru_2O_7., Comment: 5 pages, 4 figures

We perform a comprehensive numerical study of d-wave Fermi surface deformations (dFSD) on a square lattice, the so-called d-wave Pomeranchuk instability, including bilayer coupling. Since the order parameter corresponding to the dFSD has Ising symmetry, there are two stacking patterns between the layeres, (+,+) and (+,-). This additional degree of freedom gives rise to a rich variety of phase diagrams. The phase diagrams are classified by means of the energy scale Lambda_{z}, which is defined as the bilayer splitting at the saddle points of the in-plane band dispersion. As long as Lambda_{z} ne 0, a major stacking pattern is usually (+,-), and (+,+) stacking is stabilized as a dominant pattern only when the temperature scale of the dFSD instability becomes much smaller than Lambda_z. For Lambda_{z}=0, the phase diagram depends on the precise form of the bilayer dispersion. We also analyze the effect of a magnetic field on the bilayer model in connection with a possible dFSD instability in the bilyared ruthenate Sr_3Ru_2O_7., Comment: 18 pages, 7 figures

We study d-wave Fermi surface deformations (dFSD), the so-called Pomeranchuk instability, on bilayer and infinite-layer square lattices. Since the order parameter of the dFSD has Ising symmetry, there are two stacking patterns along the c axis: (+,+) and (+,-). We find that, as long as the c axis dispersion is finite at the saddle points of the in-plane band dispersion, the (+,-) stacking is usually favored independently on the details of interlayer coupling, yielding no macroscopic anisotropy. The dFSD provides unique spontaneous symmetry breaking that is self-masked in layer materials., Comment: 5 pages, 3 figures, published version

Recently, a strongly enhanced xy anisotropy of magnetic excitations was observed in YBa_2Cu_3O_y (YBCO_y) with y=6.45 and Tc=35 K [Science 319, 597 (2008)]. Unlike the observation in YBCO_6.6 and YBCO_6.85, the anisotropy grows to be pronounced at lower temperature and at lower energy, and is not suppressed by the onset of superconductivity. We propose that the effect of singlet pairing is substantially reduced in YBCO_6.45. This reduction concomitantly enhances an order competing with singlet pairing, a strong tendency of the so-called d-wave Pomeranchuk instability, leading to the magnetic excitations observed experimentally., Comment: 11 pages, 4 figures, published version

We study magnetic field effects on spontaneous Fermi surface symmetry breaking with d-wave symmetry, the so-called d-wave "Pomeranchuk instability''. We use a mean-field model of electrons with a pure forward scattering interaction on a square lattice. When either the majority or the minority spin band is tuned close to the van Hove filling by a magnetic field, the Fermi surface symmetry breaking occurs in both bands, but with a different magnitude of the order parameter. The transition is typically of second order at high temperature and changes to first order at low temperature; the end points of the second order line are tricritical points. This qualitative picture does not change even in the limit of a large magnetic field, although the magnetic field substantially suppresses the transition temperature at the van Hove filling. The field produces neither a quantum critical point nor a quantum critical end point in our model. In the weak coupling limit, typical quantities characterizing the phase diagram have a field-independent single energy scale while its dimensionless coefficient varies with the field. The field-induced Fermi surface symmetry breaking is a promising scenario for the bilayer ruthenate Sr3Ru2O7, and future issues are discussed to establish such a scenario., Comment: 28 pages, 9 figures

We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a d-wave Pomeranchuk instability and a BCS pairing interaction driving d-wave superconductivity. Tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing., Comment: 14 pages, 10 figures

The most salient features observed around a metamagnetic transition in Sr3Ru2O7 are well captured in a simple model for spontaneous Fermi surface symmetry breaking under a magnetic field, without invoking a putative quantum critical point. The Fermi surface symmetry breaking happens in both a majority and a minority spin band but with a different magnitude of the order parameter, when either band is tuned close to van Hove filling by the magnetic field. The transition is second order for high temperature T and changes into first order for low T. The first order transition is accompanied by a metamagnetic transition. The uniform magnetic susceptibility and the specific heat coefficient show strong T dependence, especially a log T divergence at van Hove filling. The Fermi surface instability then cuts off such non-Fermi liquid behavior and gives rise to a cusp in the susceptibility and a specific heat jump at the transition temperature., Comment: 11 pages, 4 figures