Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

Vojta, Matthias

doi:10.1080/00018730903122242

Cited by 474 publications

(603 citation statements)

References 534 publications

(587 reference statements)

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“…In this still SC state the filaments constitute snake-like paths through an SDW background with an average density of almost one electron per site. These textures provide a link to the study of disordered (quenched) stripes similar to those discussed recently within various GL models [35][36][37]. Therefore, depending upon the correlation strength and the details of the disorder, the magnetic ordering temperature T g can vary significantly, and the ordering itself can be droplet or filamentary-like.…”

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confidence: 59%

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

et al. 2010

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Abstract. In underdoped high-T c cuprates, d-wave superconductivity competes with antiferromagnetism. It has generally been accepted that suppressing superconductivity leads to the nucleation of spin-density wave (SDW) order with wavevector near (π, π). We show theoretically, for a d-wave superconductor in an applied magnetic field including disorder and electronic correlations, that the creation of SDW order is in fact not simply due to suppression of superconductivity, but rather due to a correlation-induced splitting of an electronic bound state arising from the sign change of the order parameter along quasiparticle trajectories. The induced SDW order is therefore a direct consequence of the d-wave symmetry. The formation of anti-phase domain walls proves to be crucial for explaining the heretofore puzzling temperature dependence of the induced magnetism as measured by neutron diffraction.A superconductor is characterized by a Bardeen-Cooper-Schrieffer (BCS) order parameter k (R), where R is the center-of-mass coordinate of a Cooper pair of electrons with momenta (k, −k). The bulk ground state of such a system is homogeneous, but a spatial perturbation that breaks pairs, e.g. a magnetic impurity, may cause the suppression of k (R) locally. What is revealed when superconductivity is suppressed is the electronic phase in the absence of k , a normal Fermi liquid. Thus the low-energy excitations near magnetic impurities and in the vortex 4 Author to whom any correspondence should be addressed. [9,10] detected magnetic ordering as a wedge-shaped extension of the 'spin glass' phase into the SC dome of the temperature versus doping phase diagram ( figure 1(a)). Lake et al [2] reported that an incommensurate magnetic order similar to the field-induced state was also observed in zero field. Although it also vanished at T c , the ordered magnetic moment in zero field had a T dependence, which was qualitatively different from the field-induced signal. The zero-field signal was attributed to disorder, but the relation between impurities and magnetic ordering remained unclear. Because strong magnetic fluctuations with similar wavevectors are reported at low but nonzero energies in inelastic neutron scattering experiments on these materials, e.g. on optimally doped LSCO samples exhibiting no spin-glass phase in zero field, it is frequently argued that impurities or vortices simply 'freeze' this fluctuating order [11].Describing such a phenomenon theoretically at the microscopic level is difficult due to the inhomogeneity of the interacting system, but it is important if one wishes to explore situations with strong disorder, where the correlations may no longer reflect the intrinsic spin dynamics of the pure system. Such an approach was proposed in a model calculation for an inhomogeneous d-wave superconductor with Hubbard-type correlations treated in the mean field [12]. In this model, a single impurity creates, at sufficiently large Hubbard interaction U and impurity potential strength V imp , a droplet of staggered magn...

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confidence: 59%

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

et al. 2010

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“…2,6,11,28,75 The detection of CO in bulk SC crystals with x far below and far above x = 1/8 is certainly the most significant finding. The full picture, however, becomes clear only when considering the relationship between the various properties and transition temperatures.…”

Section: Discussionmentioning

confidence: 95%

“…Among the debated interpretations is the so-called stripe model in which the charge carriers in the CuO 2 planes segregate into hole rich stripes, thus forming antiphase boundaries between intermediate spin stripes with locally AF correlations. 12,[26][27][28] In the LTT phase, which breaks the fourfold rotational symmetry of the individual CuO 2 planes, the electron-lattice coupling is believed to play a central role in the pinning of stripes, [29][30][31][32][33] although recent experiments under pressure revealed that stripes can break the symmetry even in the absence of long range LTT order. 34 So far, La 1.6−x Nd 0.4 Sr x CuO 4 is the only system with stripe-ordered LTT phase where magnetic and charge order have been studied with diffraction on both sides of x = 1/8.…”

Section: Introductionmentioning

confidence: 99%

Stripe order in superconducting La2−xBaxCuO
Hücker
¹
,
Zimmermann
²
,
Gu
³

et al. 2011
Phys. Rev. B
308
43
411
2
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The correlations between stripe order, superconductivity, and crystal structure in La2−x Bax CuO4 single crystals have been studied by means of x-ray and neutron diffraction as well as static magnetization measurements. The derived phase diagram shows that charge stripe order (CO) coexists with bulk superconductivity in a broad range of doping around x = 1/8, although the CO order parameter falls off quickly for x = 1/8. Except for x = 0.155, the onset of CO always coincides with the transition between the orthorhombic and the tetragonal low temperature structures. The CO transition evolves from a sharp drop at low x to a more gradual transition at higher x, eventually falling below the structural phase boundary for optimum doping. With respect to the interlayer CO correlations, we find no qualitative change of the stripe stacking order as a function of doping, and in-plane and out-of-plane correlations disappear simultaneously at the transition. Similarly to the CO, the spin stripe order (SO) is also most pronounced at x = 1/8. Truly static SO sets in below the CO and coincides with the first appearance of in-plane superconducting correlations at temperatures significantly above the bulk transition to superconductivity (SC). Indications that bulk SC causes a reduction of the spin or charge stripe order could not be identified. We argue that CO is the dominant order that is compatible with SC pairing but competes with SC phase coherence. Comparing our results with data from the literature, we find good agreement if all results are plotted as a function of x ′ instead of the nominal x, where x ′ represents an estimate of the actual Ba content, extracted from the doping dependence of the structural transition between the orthorhombic phase and the tetragonal high-temperature phase.

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“…Detwinned single crystals of YBa 2 Cu 3 O 6.51 (ortho-II, Tc = 57 K, doping concentration p ∼ 0.1) and YBa 2 Cu 3 O 6.67 (ortho-VIII, Tc = 67 K, p ∼ 0.12) were studied. We note that YBCO crystals generally belong to the cleanest available cuprate among the different families (31). The single crystals were obtained from flux growth (32).…”

Section: Methodsmentioning

confidence: 99%

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

Jang

Lee

Nojiri

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

122

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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...

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Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

Cited by 474 publications

References 534 publications

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

Stripe order in superconducting La2−xBaxCuO
Hücker
¹
,
Zimmermann
²
,
Gu
³

et al. 2011
Phys. Rev. B
308
43
411
2
View full text Add to dashboard Cite

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

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Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

Cited by 474 publications

References 534 publications

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

d-Wave superconductivity as a catalyst for antiferromagnetism in underdoped cuprates

Stripe order in superconducting La2−xBaxCuOHücker1, Zimmermann2, Gu3 et al. 2011Phys. Rev. B308434112View full textAdd to dashboardCite

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

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Stripe order in superconducting La2−xBaxCuO
Hücker
¹
,
Zimmermann
²
,
Gu
³

et al. 2011
Phys. Rev. B
308
43
411
2
View full text Add to dashboard Cite