The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction

Forgan, E. M.; Blackburn, E.; Holmes, A. T.; Briffa, A. K. R.; Chang, J.; Bouchenoire, Laurence; Brown, S. D.; Liang, Ruixing; Bonn, D. A.; Hardy, W. N.; Christensen, Niels Bech; Zimmermann, M. v.; Hücker, M.; Hayden, Stephen M

doi:10.1038/ncomms10064

Cited by 98 publications

(142 citation statements)

References 31 publications

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“…59 followed by uni-axial CDW reconstruction with Q = (δ,0,0), and where δ ≈ 0.3 according to X-ray scattering measurements. 9 Multiple Fermi surface sections, between which magnetic breakdown is possible, 17,24,39,40 are present after reconstruction: for clarity we color only one section resistivity is not a linear function of the interlayer hopping parameters: combining all three symmetry warpings onto a single section of Fermi surface cannot reproduce the data.…”

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confidence: 99%

Broken rotational symmetry on the Fermi surface of a high-Tc superconductor

et al. 2017

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Broken fourfold rotational (C4) symmetry is observed in the experimental properties of several classes of unconventional superconductors. It has been proposed that this symmetry breaking is important for superconducting pairing in these materials, but in the high-Tc cuprates this broken symmetry has never been observed on the Fermi surface. Here we report a pronounced anisotropy in the angle dependence of the interlayer magnetoresistance of the underdoped high transition temperature (high-Tc) superconductor YBa2Cu3O6.58, directly revealing broken C4 symmetry on the Fermi surface. Moreover, we demonstrate that this Fermi surface has C2 symmetry of the type produced by a uniaxial or anisotropic density-wave phase. This establishes the central role of C4 symmetry breaking in the Fermi surface reconstruction of YBa2Cu3O6+δ , and suggests a striking degree of universality among unconventional superconductors.

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confidence: 99%

Broken rotational symmetry on the Fermi surface of a high-Tc superconductor

et al. 2017

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“…The dome-shaped region of d-symmetry Cooper-paired high-temperature superconductivity is universally accepted. More recently, an unusual density wave state has been detected by bulk probes [4][5][6][7][8][9][10][11][12][13] in the region indicated schematically in pink; its modulations are now known to have a d-symmetry form factor [14][15][16] . The range of hole density, p, in which d-symmetry form factor density waves are studied in this paper is indicated by the white double-headed arrow.…”

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“…1a. Figure 1b,c exemplifies the predominately d-symmetry form factor [14][15][16] of this DW when imaged directly. One obstacle to understanding this dFF-DW state is that large-field-of-view sublattice-resolved images of cuprate electronic structure 14 …”

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“…Of course, electronlattice interactions can also play a significant role, with the coupling to the B 1g modes long being of foremost interest 19,20,38 . Strong interactions of this mode with the electrons 39 ultimately leading to static, finite-Q lattice distortions with d-symmetry form factor 15 have recently been discovered in association with the cuprate dFF-DW state. Nevertheless, electron-lattice interactions are not by themselves sufficient to explain the phase diagram of the dFF-DW (refs 11-13) because, for example, they also exist in the overdoped regime where the dFF-DW is absent.…”

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“…Specifically for a DW occurring at Q, one can then evaluate the magnitude of its d-symmetry form factorD(Q) and its s -and s-symmetry form factorsS (Q) andS(Q), respectively. Studies of non-energy-resolved R(r, E) images using this approach have revealed that the DW modulations in the O x (r) and O y (r) sublattice images of electronic structure in underdoped Bi 2 Sr 2 CaCu 2 O 8+x and Ca 2−x Na x CuO 2 Cl 2 consistently exhibit a relative phase of π and therefore a predominant d-symmetry form factor 14 ; X-ray scattering studies 15,16 yield the same conclusion for two other cuprates, YBa 2 Cu 3 O 7−x and Bi 2 Sr 2−x La x CuO 6+δ . Such X-ray scattering studies now generally report a short-ranged density wave with wavevector centred around Q = (Q, 0); (0, Q) occurring approximately in the pink shaded regions [11][12][13] of the schematic phase diagram in Fig.…”

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Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

et al. 2015

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Research on high-temperature superconducting cuprates is at present focused on identifying the relationship between the classic 'pseudogap' phenomenon 1,2 and the more recently investigated density wave state 3-13 . This state is generally characterized by a wavevector Q parallel to the planar Cu-O-Cu bonds 4-13 along with a predominantly d-symmetry form factor 14-16 (dFF-DW). To identify the microscopic mechanism giving rise to this state 17-29 , one must identify the momentum-space states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization 14 of electronic structure and reveal that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy ∆ 1 . Moreover, we demonstrate that the dFF-DW modulations at E = −∆ 1 (filled states) occur with relative phase π compared to those at E = ∆ 1 (empty states). Finally, we show that the conventionally defined dFF-DW Q corresponds to scattering between the 'hot frontier' regions of momentum-space beyond which Bogoliubov quasiparticles cease to exist [30][31][32] . These data indicate that the cuprate dFF-DW state involves particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in momentum space where the pseudogap opens.A conventional 'Peierls' charge density wave (CDW) in a metal results from particle-hole interactions which open an energy gap at specific regions of k-space that are connected by a common wavevector Q. This generates a modulation in the density of free charge at Q along with an associated modulation of the crystal lattice parameters. Such CDW states are now very well known 33 . In principle, a density wave modulating at Q can also exhibit a 'form factor' (FF) with different possible symmetries 34,35 (see Supplementary Section 1). This is relevant to the high-temperature superconducting cuprates because numerous researchers have recently proposed that the 'pseudogap' regime 1,2 (PG in Fig. 1a) contains an unconventional density wave with a d-symmetry form factor [17][18][19][20][21][22][23][24][25][26][27][28][29] . The basic phenomenology of such a state is that intraunit-cell (IUC) symmetry breaking renders the O x and O y sites within each CuO 2 unit-cell electronically inequivalent, and that this inequivalence is then modulated periodically at wavevector Q parallel to (1,0);(0,1). The real-space (r-space) schematic of such a d-symmetry FF density wave (dFF-DW) at Q x , as shown in Fig. 1b, exemplifies periodic modulations at the O x sites that are π out of phase with those at the O y sites. Such a state is then described by A(r) = D(r) cos(φ(r) + φ 0 (r)), where A(r) represents whatever is the modulating electronic degree of freedom, φ(r) = Q x · r is the DW spatial phase at location r, φ 0 (r) represents disorde...

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The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction

Cited by 98 publications

References 31 publications

Broken rotational symmetry on the Fermi surface of a high-Tc superconductor

Broken rotational symmetry on the Fermi surface of a high-Tc superconductor

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

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