How coherent quasiparticles emerge by doping quantum antiferromagnets is a key question in correlated electron systems, whose resolution is needed to elucidate the phase diagram of copper oxides. Recent resonant inelastic X-ray scattering (RIXS) experiments in hole-doped cuprates have purported to measure high-energy collective spin excitations that persist well into the overdoped regime and bear a striking resemblance to those found in the parent compound, challenging the perception that spin excitations should weaken with doping and have a diminishing effect on superconductivity. Here we show that RIXS at the Cu L 3 -edge indeed provides access to the spin dynamical structure factor once one considers the full influence of light polarization. Further we demonstrate that high-energy spin excitations do not correlate with the doping dependence of T c , while low-energy excitations depend sensitively on doping and show ferromagnetic correlations. This suggests that high-energy spin excitations are marginal to pairing in cuprate superconductors.

High-temperature superconductivity (HTSC) mysteriously emerges upon doping holes 1 or electrons 2 into insulating copper oxides with antiferromagnetic (AFM) order. It has been thought that the large energy scale of magnetic excitations, compared to phonon energies for example, lies at the heart of an electronically-driven superconducting phase with high transition temperatures (T c ) 3-5 . Comparison of high-energy magnetic excitations of hole-and electron-doped superconductors in connection with the respective T c provides an exceptional, yet un-capitalized opportunity to test this hypothesis 6-9 . Here, we use resonant inelastic x-ray scattering (RIXS) at the Cu L 3 -edge 10,11 to reveal high-energy collective excitations in the archetypical electron-doped cuprate Nd 2-x Ce x CuO 4 (NCCO) 2 . Surprisingly, despite the fact that the AFM correlations are short-ranged 12 , magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates 6,7 . Furthermore, we find an unexpected and highly dispersive branch of collective modes in superconducting NCCO that are absent in hole-doped compounds. These modes emanate from zone center and weaken with increasing temperature, which signal a quantum phase distinct from superconductivity. The asymmetry uncovered between electron-and hole-doped cuprates provides new, unexpected dimensions to collective excitations that are generally important to the mechanism of superconductivity in these materials. Hole-doped cuprates display compelling evidence for the surprising persistence of magnetic excitations beyond the AFM phase boundary 6,7 , as well as the existence of symmetrybroken phases, such as charge density waves 13,14,15 and orbital loop currents 16 , distinct from superconductivity. Whether these are universal and exist on the other side of the cuprate phase diagram, i.e. with electron-doping, remains an important open question. To address this issue,

If the pseudogap and superconducting order parameters compete within a GinzburgLandau framework, this should be detectable as an abrupt change in the spectral-weight transfer at T c . To search for this signature, we performed measurements of the electronic states in Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES), which directly probes the occupied states of the single-particle spectral function. ARPES is an ideal tool for this study because it can resolve the strong momentum anisotropies of the pseudogap and superconducting gap, both of which become the largest at the antinode, the Fermi momentum (k F ) on the Brillouin zone boundary (Fig. 1b).We show in Fig. 1a a detailed temperature dependence of the ARPES spectra at the antinode of optimally-doped Bi2212 (denoted OP98, p ~ 0.160, T c = 98 K). Here, all the spectra are divided by the resolution-convolved Fermi-Dirac function (FD) to effectively remove the Fermi cutoff. At T << T c , the spectra show a "peak-dip-hump" structure which is typical for the cuprates near the antinode. While the peak (blue circles) is a signature of superconductivity, the dip (purple down triangles) and hump (red squares) are often associated with strong band renormalizations arising from electron-boson coupling. 21,22 Above T c , the spectra show a continued suppression of spectral intensity at the Fermi level (E F ), defining the pseudogap.1 Notably, the peak feature becomes weaker but survives above T c . There is no singular signature in the spectral lineshape at T c over a wide doping range (Supplementary Fig. 1 for complete dataset). The non-trivial evolution of the spectral lineshape has been making the interpretation of the pseudogap difficult.To investigate the nature of the peak, dip and hump, we show in Fig. 1c their energies as a function of temperature. The energy scale of the anomalously broad hump feature at T c < T < T* decreases with increasing temperature and hole doping ( Supplementary Fig. 1), suggesting that it arises from the pseudogap. The hump at T > T c continuously connects with that at T < T c (Fig. 1c), suggesting that not only the electron-boson coupling but also the pseudogap affects the hump energy at T < T c while simultaneously coexisting with the superconducting peak. Here, a simple addition of two gaps in quadrature does not reproduce the data and does not capture the mixed nature of the all spectral features as noted earlier. 15Next, we show in Figs. 1d-1f the spectral weight obtained by analyzing the spectral intensity I(ω) at the antinode (Fig. 1a), where ω is energy. and high-energy spectral weights, respectively Because the energy scale for superconductivity is < 50 meV, the opening of a superconducting gap at k F should push the 1 st moment energy away from E F in a narrow range, and have almost no effect on the low-and high-energy spectral weights.In contrast with the behavior expected for homogeneous superconductivity, the most striking signature in the current result is the spectral-weight singular...

Charge and spin density waves, periodic modulations of the electron, and magnetization densities, respectively, are among the most abundant and nontrivial low-temperature ordered phases in condensed matter. The ordering direction is widely believed to result from the Fermi surface topology. However, several recent studies indicate that this common view needs to be supplemented. Here, we show how an enhanced electron-lattice interaction can contribute to or even determine the selection of the ordering vector in the model charge density wave system ErTe 3 . Our joint experimental and theoretical study allows us to establish a relation between the selection rules of the electronic light scattering spectra and the enhanced electron-phonon coupling in the vicinity of band degeneracy points. This alternative proposal for charge density wave formation may be of general relevance for driving phase transitions into other brokensymmetry ground states, particularly in multiband systems, such as the iron-based superconductors.electron-phonon interactions | nonconventional mechanism | Raman spectroscopy | solid-solid phase transitions T he common view of charge density wave (CDW) formation was originally posed in the work by Kohn (1). Using Kohn's reasoning (1), the tendency to ordering is particularly strong in low dimensions, because the Fermi surface has parallel parts, referred to as nesting. This nesting leads to a divergence in the Lindhard susceptibility, determining the magnitude and direction of the ordering vector Q (2). This divergence in the electronic susceptibility is conveyed to the lattice by the electron-phonon coupling: a phonon softens to zero frequency at Q, and a static lattice distortion develops when the system enters the CDW state, a behavior known as the Kohn anomaly.However, several publications raise the question as to whether nesting alone is sufficient to explain the observed ordering direction Q (3-7), particularly in dimensions higher than 1D. A central question is whether the selection of the CDW ordering vector is always driven by an electronic instability or if the ordering vector could, instead, be determined by a lattice distortion driven by some other mechanism exploiting the role of the electron-phonon coupling. In the latter case, the selected ordering vector would not necessarily nest the Fermi surface. The importance of strongly momentum-dependent electron-phonon coupling on CDW formation was pointed out in refs. 3 and 4, where the relevance of the Fermi surface for determining the ordering vector was indeed found to decrease as the coupling strength increases. In a recent paper on inelastic X-ray scattering measurements on 2H-NbSe 2 , acoustic phonons were observed to soften to zero frequency over an extended region around the CDW ordering vector (8). The authors argue that this behavior is not consistent with a Kohn anomaly picture, where sharp dips are expected (8). Therefore, the phonon softening must be driven by another mechanism, which they identify as a wave vector-dependent e...

We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established, and where there are signatures of a possible metallic phase.PACS numbers: 71.10. Fd, 71.30.+h, 71.45.Lr, The electron-phonon (el-ph) interaction is responsible for many phenomena in condensed matter physics, including charge density waves (CDWs) and conventional superconductivity. While the el-ph interaction is well understood in metals, the role of phonons in strongly correlated systems is less clear, in part because the interplay of strong electron-electron (el-el) and el-ph interactions can lead to competing ordered phases. Despite its difficulty, this is an important problem to solve because multiple experimental probes have detected signatures of significant lattice effects in strongly correlated materials. For example, in the cuprate high-temperature superconductors, angle-resolved photoemission spectroscopy (ARPES) has observed "kinks" in the band dispersion, which have been attributed to the el-ph interaction, 1 as well as small polaron formation in undoped Ca 2−x Na x CuOCl 2 . 2,3 Additional evidence for a significant el-ph interaction include strong quasiparticle renormalizations detected by STM, 4 and studies which have qualitatively reproduced optical conductivity peaks by including phonons. 5,6 Besides the cuprates, other materials with both strong el-el and el-ph interactions include the manganites 7 and fullerenes. 8On general grounds, two effects are expected when elph interactions are included in a system with strong el-el repulsion. The first is that the two interactions renormalize each other. The phonons mediate a retarded attractive el-el interaction, thus reducing the effective Coloumb repulsion, while the el-el repulsion suppresses charge fluctuations, and hence the el-ph interaction, which couples to them. The second effect is a reduction in the quasiparticle weight due to additional scattering processes, which at large el-ph couplings can lead to a polaron crossover.A natural model for studying the interplay of the elel and el-ph interactions is the Hubbard-Holstein (HH) model, which has been studied using various numerical approaches producing sometimes contradicting results. Within dynamical mean field theory (DMFT), the suppression of the el-ph interaction depends on the underlying phase, and antiferromagnetic (AFM)-DMFT has found a moderate increase i...

We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.

Hybrid improper ferroelectricity, where an electrical polarization can be induced via a trilinear coupling to two non-polar structural distortions of different symmetry, has recently been experimentally demonstrated for the first time in the n=2 Ruddlesden-Popper compound Ca3Ti2O7. In this paper we use group theoretic methods and first-principles calculations to identify possible ferroelectric switching pathways in Ca3Ti2O7. We identify low-energy paths that reverse the polarization direction by switching via an orthorhombic twin domain, or via an antipolar structure. We also introduce a chemically intuitive set of local order parameters to give insight into how these paths are relevant to switching nucleated at domain walls. Our findings suggest that switching may proceed via more than one mechanism in this material.

Angle-resolved photoemission spectroscopy (ARPES) probes the momentum-space electronic structure of materials and provides invaluable information about the high-temperature superconducting cuprates 1. Likewise, scanning tunnelling spectroscopy (STS) reveals the cuprates' real-space inhomogeneous electronic structure. Recently, researchers using STS have exploited quasiparticle interference (QPI)-wave-like electrons that scatter off impurities to produce periodic interference patterns-to infer properties of the quasiparticles in momentum space. Surprisingly, some interference peaks in Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) are absent beyond the antiferromagnetic zone boundary, implying the dominance of a particular scattering process 2. Here, we show that ARPES detects no evidence of quasiparticle extinction: quasiparticle-like peaks are measured everywhere on the Fermi surface, evolving smoothly across the antiferromagnetic zone boundary. This apparent contradiction stems from differences in the nature of single-particle (ARPES) and two-particle (STS) processes underlying these probes. Using a simple model, we demonstrate extinction of QPI without implying the loss of quasiparticles beyond the antiferromagnetic zone boundary. Recently, STS has been used to infer momentum-space information from the Fourier transform of the position (r)-and energy (ω)-dependent local density of states (LDOS), ρ(r,ω) (refs 3-6). Conventionally, a superconductor has well-defined momentum eigenstates (that is, Bogoliubov quasiparticles), so ρ(r,ω) is spatially homogeneous. However, scattering from inhomogeneities often present in the cuprates 7 mixes momentum eigenstates and QPI manifests itself as a spatial modulation of ρ(r,ω) with well-defined wave vector q, appearing in the Fourier transform, ρ(q,ω). QPI experiments are interpreted using the octet model 3-6 , positing that wave vectors q 1−7 connecting the ends of 'banana shaped' contours of constant energy (CCEs) dominate ρ(q,ω). Dispersing wave vectors are associated with coherent superconducting quasiparticles and the evolution of q 1−7 as a function of bias voltage is used to infer the Fermi surface and the magnitude of the d-wave superconducting gap. QPI experiments have found that the intensity of some of the peaks in ρ(q,ω) vanishes on approaching the diagonal line between (0,π) and (π,0) (corresponding to the antiferromagnetic zone boundary) 5. These results lead naturally to speculation about the disappearance of QPI and possible extinction of quasiparticles themselves near the boundary of the Brillouin zone (antinodal region). Notably, ARPES has long shown antinodal quasiparticles below the critical temperature T c in Bi-2212 over a wide doping range