Igor Vinograd and Marc-Henri Julien, LNCMI Grenoble.
The ubiquity of charge-density waves (CDW) in cuprate superconductors is now well established, but the mechanism responsible for their formation remains debated. The generic aspects of the microscopic structure of the CDW are not settled yet. In this work, we used 17O nuclear magnetic resonance (NMR) to study the CDW order observed upon the application of a magnetic field in the superconducting state of YBa2Cu3Oy (YBCO). Previous measurements have established that this CDW is long-range ordered in all three spatial dimensions (“3D”) with a single propagation vector q (“unidirectional”) along the crystallographic b axis (YBCO is an orthorhombic material). While x-ray scattering measurements have found that q is incommensurate, we show here that the CDW is actually commensurate at the local scale, as probed by NMR. We find a real-space periodicity of three unit cells (i.e., λ = 3b and q = 1/3 in units of 2π/b, where b is the lattice parameter along the b axis). A similar dichotomy between a commensurate local and an incommensurate global propagation vector was previously reported in CDW systems such as dichalcogenides, manganites, and in a cuprate (Bi2212). The origin of this dichotomy generally lies in the presence of phase slips (so-called discommensurations) that result from the interplay between an incommensurate tendency at long length scale and a commensuration effect at short length scale. The former arises from properties of the Fermi surface and/or long-range Coulomb repulsion while the latter may be due to electron-electron interactions [as argued for Bi2212 in Mesaros et al. PNAS 113, 12661 (2016)] or lock-in to the lattice as the different CDW periods for YBCO (three unit cells) and for Bi2212 (four unit cells) most naturally suggest. Being devoid of disorder, magnetic ordering, and competition with superconductivity, the high-field CDW of YBCO is likely to represent the “ideal” cuprate CDW, which appears to be oxygen centered, unidirectional, and globally incommensurate while locally locked to the lattice.
Figure: Second high-frequency satellite of O(2) sites in YBa2Cu3O656 in the high-field CDW phase (T = 2 K, Bz = 27.1 T). Two asymmetric peaks, OA and OB , having 2:1 relative areas, consistent with a local CDW period of three unit cells, describe the line shape.
Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy , I. Vinograd, R. Zhou, M. Hirata, T. Wu, H. Mayaffre, S. Krämer, R. Liang, W. N. Hardy, D. A. Bonn, and M.-H. Julien, Nat. Commun. 12, 3274 (2021).
