Pb${}_{10-x}$Cu${}_x$(PO${}_4$)${}_6$O: a Mott or charge transfer insulator in need of further doping for (super)conductivity

We briefly review the status quo of research on the putative superconductor Pb${}_9$Cu(PO${}_4$)${}_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from substituting Pb by Cu and thus differs from LK-99) is required to make it metallic and potentially superconducting.