We report resonant inelastic x-ray measurements of insulating La2CuO4 and Sr2CuO2Cl2 taken with the incident energy tuned near the Cu K absorption edge. We show that the spectra are well described in a shakeup picture in 3rd order perturbation theory which exhibits both incoming and outgoing resonances, and demonstrate how to extract a spectral function from the raw data. We conclude by showing q-dependent measurements of the charge transfer gap.PACS numbers: 78.70. Ck, 74.25.Jb Inelastic x-ray scattering (IXS) has shown promise as a practical probe of electronic excitations in condensed matter because of its broad kinematic range and direct coupling to the electron charge. However, since x-rays are strongly absorbed in high density materials, successful applications of the technique have been limited to low-Z systems [1,2,3,4,5].Several recent studies [6,7,8,9], have shown that by that by tuning the incident energy near an x-ray absorption edge a Raman effect could be measured, despite the high absorption, because of the resonant enhancement. These studies have emphasized the role of coulomb interactions in the scattering process. Since it involves coupling between highly excited virtual states and strongly correlated valence states, it is important to characterize the resonance process well for the technique to be useful.With emphasis on systematics, we have measured resonant inelastic x-ray scattering at moderate resolution (∆E=0.9 eV) near the CuK absorption edge in the high-T c parent insulator La 2 CuO 4 (LCO) as a function of incident photon energy. Based on the changes of inelastic intensity and peak position with incident energy we show that the scattering is well described in a "shakeup" picture in 3rd order perturbation threoy [10]. We also present higher resolution measurements (∆E=0.45 eV) on another insulator, Sr 2 CuO 2 Cl 2 (SCOC), as a function of momentum transfer, q, which show some new features, such as the 2 eV optical charge transfer gap.Experiments were carried out at the X21 wiggler line at the National Synchrotron Light Source and the 3ID (SRI-CAT) undulator line at the Advanced Photon Source. At X21 the energy resolution was 0.45 eV and typical count rates were 0.4 Hz. At 3ID with 0.9 eV resolution 9 Hz was typical. The scattered light was collected with a spherical, diced, Ge(733) analyzer and imaged onto a detector. Energy analysis was done by rotating the analyzer and translating the detector in coincidence. The momentum transfer was varied by rotating the entire apparatus around the scattering center (exact experimental geometries are indicated in the figure captions). −1 parallel toĉ. The upper frame shows the raw spectra plotted against transferred energy (curves are offset for clarity). In the lower frame the open and filled circles are the inelastic peak height and position, respectively, plotted against incident energy. The black line is the fluorescence yield which peaks at the Cu1s → 4p energy.The LCO and SCOC crystals were grown by techniques described previously [11,12]....

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa 2 Cu 3 Ox (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field (H c2 ) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO 2 planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to H c2 , given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an "ideal" disorder-free cuprate.high-temperature superconductors | charge-density-wave order | high magnetic field X-ray scattering | vestigial nematic order | competing order C harge-density-wave (CDW) order has been found to exist universally in the hole-doped superconducting cuprates (1-18), and the common characteristics at zero magnetic field include bidirectionality, quasi-2D and short-ranged correlations (7-17). More specifically, the CDW diffraction patterns are found in both directions of Cu-O bonds in the CuO2 plane (Fig. 1A), and the CDW correlation lengths parallel and perpendicular to the planes (i.e., along the a-or b-axes and the c axis) are less than ∼ 20 and ∼ 1 lattice constants, respectively (7-16), corresponding to a correlation volume of order 10 2 unit cells (UCs). Thus, the properties of the quasi-2D CDW are likely strongly affected by disorder and only indirectly represent the true nature of the underlying CDW correlations. Indeed, X-ray scattering shows that the onset of the quasi-2D order is gradual without a sharp transition (7-17), consistent with the influence of quenched disorder on an incommensurate CDW (19-21). Furthermore, whereas Y-based and La-based cuprates exhibit a clear competition between CDW and superconductivity (7,8,(12)(13)(14)(15), such competition is not apparent in the families of Bi-based and Hg-based cuprate compounds (9-11)-a discrepancy that probably reflects different degrees of quenched disorder among cuprate families.Recently, a CDW with significantly longer correlation lengths was observed in superconducting YBCO (Fig. 1B) via X-ray scattering at high magnetic fields (13,14). This reveals the character (i.e., 3D) of the high-field charge ordering previously inferred by other measurements (3-6). At a magnetic field of ∼ 30 T, i...

We report a resonant inelastic x-ray scattering study of the dispersion relations of charge transfer excitations in insulating La2CuO4. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of ∼ 2.2 eV at the zone center, and a dispersion of ∼ 1 eV. The spectral weight of this mode becomes dramatically smaller around (π, π). The second peak shows a smaller dispersion (∼ 0.5 eV) with a zone-center energy of ∼ 3.9 eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.PACS numbers: 74.25.Jb, 74.72.Dn, 78.70.Ck, Understanding strongly correlated electron systems, such as the cuprate superconductors, remains at the heart of much of current condensed matter research. As a first step toward elucidating electron correlation effects in these systems, it is important to study the behavior of elementary excitations using various spectroscopic tools. For example, angle resolved photoemission spectroscopy (ARPES) has become an indispensable probe for studying the excitation spectrum of a single quasiparticle [1,2], while inelastic neutron scattering has been invaluable in the investigation of low-energy collective modes (1 ∼ 100 meV), such as phonons and magnons [3]. However, to date only limited information has been available on collective excitations at an energy scale on the order of ∼ 1 eV. This is unfortunate, since in this energy range, the electron dynamics are governed directly by the various hopping integrals and by the Coulomb interaction. Thus, an investigation of the dispersion relations of such collective charge excitations would yield invaluable information for any microscopic theory of charge dynamics in the copper oxides.In this Letter, we present a detailed study of the momentum-dependence of the charge excitations in La 2 CuO 4 , utilizing resonant inelastic x-ray scattering (RIXS). In the simplest picture of this insulating cuprate, the ground state consists of one hole per copper ion (Cu 2+ ), and the low-lying electronic excitations include excitons formed via a charge-transfer (CT) process, in which charge is moved from the oxygen onto the copper [4,5,6]. Specifically, an electron-hole pair, created by exciting an electron from the valence band -the ZhangRice (ZR) band [7] -to the conduction band across the CT gap, can form a bound exciton state as a result of the Coulomb interaction. This CT exciton is expected to have a large dispersion, since it has zero spin and can move without disturbing the antiferromagnetic order of the copper oxide plane. Consistent with this, our highresolution measurements have enabled us to identify an exciton-like feature at 2.2 eV with a dispersion of 1 eV. In addition, a second peak at slightly higher energy is also observed. This has a zone-center energy of 3.9 eV and a dispersion of 0.5 eV. Finally, we also discuss a dramatic reduction in spectral weight of the CT exciton observed near the (π π) position.The RIXS technique in the hard...

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Recent measurements have found nonclassical rotational inertia ͑NCRI͒ in solid 4 He starting at T ϳ 200 mK, leading to speculation that a supersolid state may exist in these materials. Differences in the NCRI fraction due to the growth method and annealing history imply that defects play an important role in the effect. Using x-ray synchrotron radiation, we have studied the nature of the crystals and the properties of the defects in solid 4 He at temperatures down to 50 mK. Measurements of peak intensities and lattice parameters do not show indications of the supersolid transition. Using growth methods similar to those of groups measuring the NCRI, we find that large crystals ͑dimensionsϳ millimeters͒ form. Scanning with a small ͑down to 10 ϫ 10 m 2 ͒ beam, we resolve a mosaic structure within these crystals, which is consistent with small-angle grain boundaries. The mosaic shows significant shifts over time even at temperatures far from melting. We discuss the relevance of these defects to the NCRI observations. Theoretical speculation about supersolidity in 4 He goes back over 40 years. While Bose-Einstein condensation ͑BEC͒ will not occur in classical solids, 1 solid helium is strongly influenced by quantum effects. Due to its large zeropoint energy and weak interatomic attraction, 4 He requires pressures of ϳ25 bar to solidify. Atoms in the solid are not well localized; vibrations due to the zero-point energy can be over 25% of the interatomic spacing. 2 Several mechanisms for bulk supersolid formation have been suggested. Andreev and Lifshitz, 3 and Chester, 4 argued that a finite concentration of vacancies might exist even at T = 0 which could then lead to a supersolid state. Leggett 5 argued that exchange could give rise to supersolidity although with a rather small supersolid fraction. While a number of experimental searches were initiated, 6 no evidence was found for a supersolid state. Several interesting effects were observed by Goodkind 7 but these results were not consistent with the standard supersolid picture.The situation changed radically in 2004 when Kim and Chan 8 reported a decrease in the moment of inertia ͓called nonclassical rotational inertia ͑NCRI͔͒ of solid 4 He in torsional oscillator ͑TO͒ experiments near 200 mK. Experiments in porous gold, Vycor, and on bulk solid all showed a NCRI of ϳ1%. NCRI has also been observed in other laboratories. 9-12 A later work 13 found that the NCRI on a rapidly frozen sample can be as much as 20% but this value was greatly reduced by annealing. On the theoretical side, path-integral Monte Carlo simulations did not find offdiagonal long-range order ͑ODLRO͒ in a defect-free hcp crystal of 4 He ͑Ref. 14͒: for a solid to be superfluid zeropoint vacancies or interstitials must be an integral part of the ground state 15 but models seem to indicate that such a state is unstable. 16 A generally puzzling feature is the high transition temperature. Consider the standard equation for the BEC for noninteracting particleswhere n is the mass per volume, h is Planck's...