Structure of the Charge-Density Wave in Cuprate Superconductors: Lessons from NMR

TL;DR

This paper combines numerical and analytical methods to interpret NMR data, revealing detailed insights into the charge-density wave structure in underdoped cuprate superconductors, and identifies key factors influencing NMR lineshapes.

Contribution

It introduces a microscopic model that accurately reproduces NMR spectra and links spectral features to Fermi surface and CDW properties in cuprates.

Findings

BdG calculations match experimental NMR spectra qualitatively

Fermi surface and CDW parameters critically influence NMR lineshapes

A hotspot model explains the origins of spectral features

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 YBa$_2$Cu$_3$O$_{6+x}$. 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.