Imaging chemical disorder in cuprates using scanning tunneling microscopy

High-T$_{c}$ cuprate superconductors are chemically, electronically and structurally inhomogeneous at the nanoscale. Although a body of theoretical work has predicted that local and global superconductivity may be dramatically impacted by particular dopant configurations, the exact positions of dopants introduced into cuprates to induce superconductivity are generally unknown. Here we use scanning tunneling microscopy to reveal the intra-unit-cell location of two different types of oxygen dopants in Bi$_{2+y}$Sr$_{2-y}$CaCu$_{2}$O$_{8+x}$. Furthermore, we show the relationship between these interstitial oxygen dopants, oxygen vacancies, and a global structural buckling known as the supermodulation. We compare our findings to theoretical simulations.