Structure of the charge density wave in cuprate superconductors: Lessons from NMR

Abstract

Using a mix of numerical and analytic methods, we show that recent NMR 17 O measurements provide detailed information about the structure of the charge-density wave (CDW) phase in underdoped YBa2Cu3O6+x. We perform Bogoliubov-de Gennes (BdG) calculations of both the local density of states and the orbitally resolved charge density, which are closely related to the magnetic and electric quadrupole contributions to the NMR spectrum, using a microscopic model that was shown previously to agree closely with x-ray experiments. The BdG results reproduce qualitative features of the experimental spectrum extremely well. These results are interpreted in terms of a generic "hotspot" model that allows one to trace the origins of the NMR lineshapes. We find that four quantities-the orbital character of the Fermi surface at the hotspots, the Fermi surface curvature at the hotspots, the CDW correlation length, and the magnitude of the subdominant CDW component-are key in determining the lineshapes. arXiv:1710.08881v3 [cond-mat.str-el]

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy

“…3 ), each with two asymmetric line shapes of equal widths. The asymmetry of the individual 17 O peaks, which is essential for a reliable fit, has been shown to arise from an inhomogeneous pattern of the local density of states (LDOS) at the Fermi level that develops alongside the high-field CDW 41 (a recent theoretical study further relates this inhomogeneous LDOS to the curvature of the Fermi surface at the hot spots 44 ). The asymmetry is determined from peaks that do not split and is thus not a fit parameter 41 .…”

“…Nonetheless, there is a huge phase space that we have not explored regarding the relative amplitude and the relative phase of the two predicted charge modulations, let alone more sophisticated scenarios with complex real space patterns. To the best of our knowledge, NMR spectra have been computed in the framework of models of charge ordering 44 , 50 but not for realistic PDW theories. When these become available, our data could be used to further test the possibility of a PDW state in YBCO in high fields.…”

Emergent charge order from correlated electron-phonon physics in cuprates

“…The rough estimates presented above for an only weak phonon-based tendency towards charge order is-in this sense -not contradicting, but it is clearly too weak to generate a long range ordered CDW state. Still, the charge order in underdoped cuprates is in fact short ranged with moderate planar correlation lengths [14][15][16] , and is most likely nucleated by defects 10,31,66 . A strong magnetic field 67,68 or uniaxial pressure 27 is needed to enhance the planar correlation length and to even achieve 3D CDW order.…”

Locally commensurate charge-density wave with three-unit-cell periodicity in YBCO

“…3), each with two asymmetric line shapes of equal widths. The asymmetry of the individual 17 O peaks, which is essential for a reliable fit, has been showed to arise from an inhomogeneous pattern of the local density of states (LDOS) at the Fermi level that develops alongside the high-field CDW [39] (a recent theoretical study further relates this inhomogeneous LDOS to the curvature of the Fermi surface at the hot spots [42]). The asymmetry is determined from peaks that do not split and is thus not a fit parameter [39].…”

“…Nonetheless, there is a huge phase space that we have not explored regarding the relative amplitude and the relative phase of the two predicted charge modulations, let alone more sophisticated scenarios with complex real space patterns. To the best of our knowledge, NMR spectra have been computed in the framework of models of charge ordering [42,48] but not for realistic PDW theories. When these beome available, our data could be used to further test the possibility of a PDW state in YBCO in high fields.…”