Dislocations as a boundary between charge density wave and oxygen rich phases in a cuprate high temperature superconductor

Multiple functional ionic and electronic orders are observed in high temperature superconducting cuprates. The charge density wave order is one of them and it is spatially localized in spatial regions of the material. It is also known that the oxygen interstitials introduced by chemical intercalation self-organize in different oxygen rich regions corresponding with hole rich regions in the Cu$O_2$ layers left empty by the charge density wave order domains. However, what happens in between these two order is not known, and neither there is a method to control this spatial separation. Here we demonstrate by using scanning nano X-ray diffraction, that dislocations or grain boundaries in the material can act as boundary between charge density wave and oxygen rich phases in a optimally doped La$_2$CuO$_4$$_+$$_y$ high temperature superconductor. Dislocations can be used therefore to control the anti-correlation of the charge density wave order with the oxygen interstitials in specific portion of the material.