Local O$_{\delta}$ probing in the high-$T_{C}$ superconductor HgBa$_{2}$CuO$_{4+\delta}$

Electric-field gradients on mercury sites of the HgBa$_{2}$CuO$_{4+\delta}$ high-$T_{C}$ superconductor were measured with the perturbed angular correlation technique and interpreted with $\textit{ab initio}$ calculations. Under oxygen annealing, an asymmetric electric-field gradient has been assigned to the presence of single oxygen atoms, O$_{\delta}$ , which are located in the Hg planes. These experiments provide an atomic scale tool for studying charge-density variations occuring in the neighborhood of the Hg atoms, which can be induced, particularly, by pointlike defects.