We report the results of a comprehensive study of charge density wave (CDW) correlations in untwinned YBa2Cu3O6+x single crystals with 0.4 ≤ x ≤ 0.99 using Cu-L3 edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for 0.45 ≤ x ≤ 0.93 (hole doping levels 0.086 p 0.163), but not for samples with x ≤ 0.44 (p 0.084) that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with x = 0.99 (p ∼ 0.19). This suggests the presence of two proximate zero-temperature CDW critical points at pc1 ∼ 0.08 and pc2 ∼ 0.18. Remarkably, pc2 is close to the doping level that is optimal for superconductivity. The CDW reflections are observed at incommensurate in-plane wave vectors (δa, 0) and (0, δ b ) with δa δ b . Both δa and δ b decrease linearly with increasing doping, in agreement with recent reports on Bibased high-Tc superconductors, but in sharp contrast to the behavior of the La2−x(Ba,Sr)xCuO4 family. The CDW intensity and correlation length exhibit maxima at p ∼ 0.12, coincident with a plateau in the superconducting transition temperature Tc. The onset temperature of the CDW reflections depends non-monotonically on p, with a maximum of ∼ 160 K for p ∼ 0.12. The RXS reflections exhibit a uniaxial intensity anisotropy. Whereas in strongly underdoped samples the reflections at (δa, 0) are much weaker than those at (0, δ b ), the anisotropy is minimal for p ∼ 0.12, and reversed close to optimal doping. We further observe a depression of CDW correlations upon cooling below Tc, and (for samples with p ≥ 0.09) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with p ∼ 0.08, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field-independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against superconductivity (Blanco-Canosa et al., Phys. Rev. Lett. 110, 187001 (2013)). We discuss the relationship of these results to prior observations of "stripe" order in La2−x(Ba,Sr)xCuO4, the "pseudogap" phenomenon, superconducting fluctuations, and quantum oscillations, as well as their implications for the mechanism of high-temperature superconductivity.

Resonant x-ray scattering clarifies the link between charge order and magnetism/superconductivity in n-doped cuprates.

We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa 2 CuO 4+δ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa 2 Cu 3 O 6+δ , the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic c axis of up to 16 T, provides information on the form factor of the CDW order. As expected from the single-CuO 2 -layer structure of Hg1201, the CDW correlations vanish at half-integer values of L and appear to be peaked at integer L. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO 2 layers.

In the underdoped regime, the cuprate high-temperature superconductors exhibit a host of unusual collective phenomena, including unconventional spin and charge density modulations, Fermi surface reconstructions, and a pseudogap in various physical observables. Conversely, overdoped cuprates are generally regarded as conventional Fermi liquids possessing no collective electronic order. In partial contradiction to this widely held picture, we report resonant X-ray scattering measurements revealing incommensurate charge order reflections for overdoped (Bi,Pb)SrCuO (Bi2201), with correlation lengths of 40-60 lattice units, that persist up to temperatures of at least 250 K. The value of the charge order wavevector decreases with doping, in line with the extrapolation of the trend previously observed in underdoped Bi2201. In overdoped materials, however, charge order coexists with a single, unreconstructed Fermi surface without nesting or pseudogap features. The discovery of re-entrant charge order in Bi2201 thus calls for investigations in other cuprate families and for a reconsideration of theories that posit an essential relationship between these phenomena.

We use polarized Raman scattering to probe lattice vibrations and charge ordering in 12 nm thick, epitaxially strained PrNiO_{3} films, and in superlattices of PrNiO_{3} with the band insulator PrAlO_{3}. A carefully adjusted confocal geometry is used to eliminate the substrate contribution to the Raman spectra. In films and superlattices under tensile strain which undergo a metal-insulator transition upon cooling, the Raman spectra reveal phonon modes characteristic of charge ordering. These anomalous phonons do not appear in compressively strained films, which remain metallic at all temperatures. For superlattices under compressive strain, the Raman spectra show no evidence of anomalous phonons indicative of charge ordering, while complementary resonant x-ray scattering experiments reveal antiferromagnetic order associated with a modest increase in resistivity upon cooling. This confirms theoretical predictions of a spin density wave phase driven by spatial confinement of the conduction electrons.

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The electronic phase behavior and functionality of interfaces and surfaces in complex materials are strongly correlated to chemical composition profiles, stoichiometry and intermixing. Here a novel analysis scheme for resonant X-ray reflectivity maps is introduced to determine such profiles, which is element specific and non-destructive, and which exhibits atomic-layer resolution and a probing depth of hundreds of nanometers.

The interplay between charge density waves (CDWs) and high-temperature superconductivity is currently under intense investigation.1-10 Experimental research on this issue is difficult because CDW formation in bulk copper-oxides is strongly influenced by random disorder, 11-13 and a long-range-ordered CDW state in high magnetic fields 14-17 is difficult to access with spectroscopic and diffraction probes. Here we use resonant x-ray scattering in zero magnetic field to show that interfaces with the metallic ferromagnet La 2/3 Ca 1/3 MnO 3 greatly enhance CDW formation in the optimally doped high-temperature superconductor YBa 2 Cu 3 O 6+δ (δ ∼ 1), and that this effect persists over several tens of nm.The wavevector of the incommensurate CDW serves as an internal calibration standard of the charge carrier concentration, which allows us to rule out any significant influence of oxygen non-stoichiometry, and to attribute the observed phenomenon to a genuine electronic proximity effect. Long-range proximity effects induced by heterointerfaces thus offer a powerful method to stabilize the charge density wave state in the cuprates, and more generally, to manipulate the interplay between different collective phenomena in metal oxides. and electron-phonon interactions, 24 but the influence of YBCO-LCMO interfaces on CDW formation has not yet been studied.Following prior RXS work on bulk YBCO, 2,4,6,18 we tuned the photon energy to the Labsorption edge of planar Cu, so that the resulting data become highly sensitive to the valence electron system in the CuO 2 planes (Fig. 1a). 18In bulk YBCO, the CDW wave vector Q CDW was found to decrease approximately linearly with the doping level, p, as expected for an instability of a hole-like Fermi surface. Cu magnetic moments at the interface), 31,32 CDW order, and superconductivity (Fig. 2).Beyond this qualitative analogy, the intensity of the RXS reflections reveals striking differences between the CDW correlations in the SLs and in the bulk. Whereas in bulk optimally doped YBCO the RXS reflections characteristic of CDW order are extremely weak, 18 their intensity in the SLs grows with increasing YBCO layer thickness (and hence increasing p ). Note that the LCMO layers are nearly transparent to x-rays in resonance to the Cu L-absorption edge, and that the YBCO volume probed in all three samples was comparable (see Methods). The systematic growth of the CDW peak intensity with thickness and its large intensity for the D = 50 nm sample demonstrate that most (if not all) of the YBCO volume in this SL is affected by CDW formation. Rather than being pinned to the interfaces, as expected for an ordinary proximity effect, these data imply that robust CDW order is present over a large fraction of the 50 nm thick layer with p = 0.15.Having established the presence of robust CDW order in the 50 nm thick YBCO layer with p = 0.15, we now turn to its temperature and magnetic field dependence. The temperature dependence of the RXS intensity (Fig. 3) is indicative of a second-order phase transi...