Broken translational and rotational symmetry via charge stripe order in underdoped YBa ₂ Cu ₃ O _{6+ y}

Abstract

Following the early discovery of stripe-like order in La-based copper-oxide superconductors, charge ordering instabilities were observed in all cuprate families. However, it has proven difficult to distinguish between uni-(stripes) and bi-directional (checkerboard) charge order in Y-and Bi-based materials.Here we use resonant x-ray scattering (RXS) to measure the two-dimensional structure factor in YBa 2 Cu 3 O 6+y , in reciprocal space. Our data reveal the presence of charge stripe order, i.e. locally unidirectional density waves, suggesting it as the true microscopic nature of charge modulations in cuprates. At the same time, we find that the well-established competition between charge order and superconductivity is stronger for charge correlations across than along the stripes, which provides additional evidence for the intrinsic unidirectional nature of the charge order.Recent studies of Y-based copper oxides have highlighted the importance of a chargeordered electronic ground state, also termed charge-density-wave (CDW), as a central element within the phenomenology of high-temperature superconductors (1-14). The family of YBa 2 Cu 3 O 6+y (YBCO) compounds have yielded a wealth of experimental results that enabled advancements in our understanding of CDW instabilities and their interplay with superconductivity (9)(10)(11)(15)(16)(17)(18)(19)(20)(21)(22).YBCO is a layered copper-oxide-based material where hole doping is controlled by the oxygen stoichiometry in the chain layer -characterized by uniaxial CuO chains running along the crystallographic b axis. In addition to ordering within the chain layer -attained via the periodic alternation of fully-oxygenated and fully-depleted CuO chains -recent experiments have extensively shown the presence of charge ordering in the CuO 2 planes, with an incommensurate wavevector Q ∼ 0.31 reciprocal lattice units (23), corresponding to a period of approximately 3 unit cells in real space (9)(10)(11). Although the stripy nature of La-based cuprates has been long 2 established (1-3), the local symmetry of the CDW in YBCO has not yet been resolved as both charge stripes (in the presence of 90• rotated domains)and checkerboard are consistent with the globally bidirectional structure of the CDW -characterized by wavevectors along both the a and b axes, at Q a ∼ (0.31, 0) and Q b ∼ (0, 0.31), respectively (10,11,(24)(25)(26). This leaves open the fundamental question as to whether stripes are the underlying charge instability in the whole class of hole-doped cuprates.Here we study the local density correlations of the charge-ordered state, and the interaction of the latter with superconductivity (SC) in underdoped YBCO, using resonant x-ray scattering (RXS). This technique, which is now at full maturity, represents a unique combination of diffraction (to probe reciprocal space) and resonant absorption (allowing element-specificity and therefore site-selectivity), and directly measures the structure factor S(Q x , Q y ), where Q x and Q y represent the momenta along the recipro...

Ideal charge-density-wave order in the high-field state of superconducting YBCO

“…The phase transition at σ = σc is rounded in an orthorhombic system, but so long as the symmetry breaking field is weak there remains a sharp cross-over from an approximately bidirectional phase (i.e., isotropic) for σ > σc to a strongly unidirectional phase for σ < σc. The bidirectional phase can still be locally stripe-like (17), but with the orientation of the stripes determined by the local disorder potential rather than by the orthorhombicity. Indeed, a strong tendency to nematic order (oriented by the weak orthorhombicity of YBCO) has been inferred from various experiments (24)(25)(26).…”

“…Although the zero-field 2D CDW is bidirectional (e.g., Fig. 1A) (16,17), it was discovered in ref. 14 that the 3D CDW in ortho-VIII is unidirectional (i.e., there is no detectable 3D CDW in the h-direction).…”

“…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)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), and the common characteristics at zero magnetic field include bidirectionality, quasi-2D and short-ranged correlations (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). More specifically, the CDW diffraction patterns are found in both directions of Cu-O bonds in the CuO2 plane (Fig.…”

“…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)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), consistent with the influence of quenched disorder on an incommensurate CDW (19)(20)(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.…”

Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor

“…Although it is known that the incommensurate charge-density-wave (CDW) order in cuprates (copper oxides) is made of ordered, stripy, nanoscale puddles with an average of only [3][4] oscillations, information about the size distribution and spatial organization of these puddles has so far not been available. We present experiments that demonstrate that CDW puddles, have a complex spatial distribution and coexist with, but are spatially anticorrelated to, quenched disorder in HgBa 2 CuO 4+y (Hg1201).…”