Why Charge Added Using Transition Metals To Some Insulators -- Including LK-99 -- Localizes and Does Not Yield a Metal

Abstract: While adding charge to semiconductors via dopants is a well-established method for tuning electronic properties, we demonstrate that introducing transition metal impurities into certain insulators can lead to localized charge, assisted by a Jahn-Teller distortion. This leads to isolated charge, and an insulating material as opposed to emergent states - including superconductivity. We focus on Cu impurities added to Pb$_{10}$(PO$_4$)$_6$O ('LK-99'), replacing 10% of Cu ions, as discussed in recent literature. Our calculations show that the material remains a wide bandgap insulator with isolated, S=1/2 localized charges on the Cu ions-similar to color centers-even within standard DFT, without the need for electron correlation corrections to the Cu d-orbitals. Superconductivity is excluded by known mechanisms that require the material to be metallic. We resolve previously observed inconsistencies between density functional theory results and experimental findings related to doping site energetics, crystal structure, and transparency. We find that Cu doping either Pb site leads to CuO$_4$ coordination and a similar unit cell volume contraction. Engineering materials with dopant sites that have different local symmetries can induce non-relativistic spin splitting-often referred to as altermagnetism. However, in the case of localized charges, this may enable spins to be individually controlled.