Impact of chain layer oxygen disorder on charge density wave order in YBa$_2$Cu$_3$O$_{6+\delta}$

Charge density wave (CDW) order in the CuO$_2$ planes of underdoped YBa$_2$Cu$_3$O$_{6+\delta}$ (YBCO) has been reported to coexist and compete with superconductivity. Here we investigate the sensitivity of the CDW order to oxygen disorder in the chain layer of YBCO using resonant soft x-ray scattering. We find that disordering the chains in o-V and o-VIII ordered YBCO$_{6.67}$ decreases the intensity of the CDW superlattice peak by a factor of $\sim2$, but unexpectedly has little effect on the incommensurability, correlation length or temperature dependence of the CDW peak. The same is true for o-III ordered YBCO$_{6.75}$, although the disordering has a smaller effect on the CDW peak intensity. The observed insensitivity of the incommensurability, correlation length and temperature dependence to chain layer oxygen disorder indicates that chain layer defects have a limited role in pinning the CDW order in the CuO$_2$ planes. We will discuss scenarios for the disorder effect, including a possible influence on CDW domain formation (CDW volume fraction) and the CDW order parameter.