Resonant X-ray scattering measurements of a spatial modulation of the Cu 3d and O 2p energies in stripe-ordered cuprate superconductors

Discovery of orbital ordering in Bi2Sr2CaCu2O8+x

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.

Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering

High T_{c} 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 to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors (La_{1.84}Sr_{0.16}CuO_{4} and Bi_{2}Sr_{1.6}La_{0.4}CuO_{6+δ}), crucially completing the picture. Interestingly, in contrast to the quasistatic 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 behavior of valence charges in hole-doped cuprates.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Nematicity and Charge Order in Superoxygenated La_{2-x}Sr_{x}CuO_{4+y}

In this Letter, we report a resonant x-ray scattering measurement of stripelike charge order in the 1/8th doped component of electronically phase-separated, orthorhombic La_{2}CuO_{4+y}. This observation is coupled to the absence of any resonant (001) peak, which at different resonant energies has been identified with the presence of low-temperature-tetragonal-like structural tilt patterns or nematicity in the CuO planes. Thus, we provide evidence that structural pinning is not necessary for the formation of static charge stripes and that the relationship between charge nematicity and stripes may not be simple.

Orbital symmetry of charge-density-wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67

Recent theories of charge-density-wave (CDW) order in high-temperature superconductors have predicted a primarily d CDW orbital symmetry. Here, we report on the orbital symmetry of CDW order in the canonical cuprate superconductors La1.875Ba0.125CuO4 (LBCO) and YBa2Cu3O6.67 (YBCO), using resonant soft X-ray scattering and a model mapped to the CDW orbital symmetry. From measurements sensitive to the O sublattice, we conclude that LBCO has predominantly s' CDW orbital symmetry, in contrast to the d orbital symmetry recently reported in other cuprates. Furthermore, we show for YBCO that the CDW orbital symmetry differs along the a and b crystal axes and that these both differ from LBCO. This work highlights CDW orbital symmetry as an additional key property that distinguishes the different cuprate families. We discuss how the CDW symmetry may be related to the '1/8-anomaly' and to static spin ordering.

Selective interlayer ferromagnetic coupling between the Cu spins in YBa2Cu3O7-x grown on top of La0.7Ca0.3MnO3

Studies to date on ferromagnet/d-wave superconductor heterostructures focus mainly on the effects at or near the interfaces while the response of bulk properties to heterostructuring is overlooked. Here we use resonant soft x-ray scattering spectroscopy to reveal a novel c-axis ferromagnetic coupling between the in-plane Cu spins in YBa2Cu3O7-x (YBCO) superconductor when it is grown on top of ferromagnetic La0.7Ca0.3MnO3 (LCMO) manganite layer. This coupling, present in both normal and superconducting states of YBCO, is sensitive to the interfacial termination such that it is only observed in bilayers with MnO2 but not with La0.7Ca0.3O interfacial termination. Such contrasting behaviors, we propose, are due to distinct energetic of CuO chain and CuO2 plane at the La0.7Ca0.3O and MnO2 terminated interfaces respectively, therefore influencing the transfer of spin-polarized electrons from manganite to cuprate differently. Our findings suggest that the superconducting/ferromagnetic bilayers with proper interfacial engineering can be good candidates for searching the theorized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in cuprates and studying the competing quantum orders in highly correlated electron systems.

Symmetry of charge order in cuprates

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

Superconductivity. Broken translational and rotational symmetry via charge stripe order in underdoped YBa₂Cu₃O(6+y)

After the discovery of stripelike order in lanthanum-based copper oxide superconductors, charge-ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between unidirectional (stripes) and bidirectional (checkerboard) charge order in yttrium- and bismuth-based materials. We used resonant x-ray scattering to measure the two-dimensional structure factor in the superconductor YBa2Cu3O(6+y) in reciprocal space. Our data reveal the presence of charge stripe order (i.e., locally unidirectional density waves), which may represent the true microscopic nature of charge modulation in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across the stripes than along them, which provides additional evidence for the intrinsic unidirectional nature of the charge order.

Impact of quenched oxygen disorder on charge density wave order in YBa2Cu3O6+x

The competition between superconductivity and charge density wave (CDW) order in underdoped cuprates has now been widely reported, but the role of disorder in this competition has yet to be fully resolved. A central question is whether disorder sets the length scale of the CDW order, for instance by pinning charge density fluctuations or disrupting an otherwise long-range order. Using resonant soft x-ray scattering, we investigate the sensitivity of CDW order in YBa2Cu3O6+x (YBCO) to varying levels of oxygen disorder. We find that quench cooling YBCO6.67 (YBCO6.75) crystals to destroy their o-V and o-VIII (o-III) chains decreases the intensity of the CDW superlattice peak by a factor of 1.9 (1.3), but has little effect on the CDW correlation length, incommensurability, and temperature dependence. This reveals that while quenched oxygen disorder influences the CDW order parameter, the spatial extent of the CDW order is insensitive to the level of quenched oxygen disorder and may instead be a consequence of competition with superconductivity.

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO2 unit cell, segregating the results into three separate electronic structure images containing only the Cu sites [Cu(r)] and only the x/y axis O sites [Ox(r) and O(y)(r)]. Phase-resolved Fourier analysis reveals directly that the modulations in the O(x)(r) and O(y)(r) sublattice images consistently exhibit a relative phase of π. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials-specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intraunit-cell states that exhibit a predominantly d-symmetry form factor.

Bond order in two-dimensional metals with antiferromagnetic exchange interactions

We present an unrestricted Hartree-Fock computation of charge-ordering instabilities of two-dimensional metals with antiferromagnetic exchange interactions, allowing for arbitrary ordering wave vectors and internal wave functions of the particle-hole pair condensate. We find that the ordering has a dominant d symmetry of rotations about lattice points for a range of ordering wave vectors, including those observed in recent experiments at low temperatures on YBa2Cu3O(y). This d symmetry implies the charge ordering is primarily on the bonds of the Cu lattice, and we propose incommensurate bond order parameters for the underdoped cuprates. The field theory for the onset of Néel order in a metal has an emergent pseudospin symmetry which "rotates" d-wave Cooper pairs to particle-hole pairs [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)]; our results show that this symmetry has consequences even when the spin correlations are short ranged and incommensurate.