Minimal model for the flat bands in copper-substituted lead phosphate apatite: Strong diamagnetism from multi-orbital physics

The claims that a copper-substituted lead apatite, denoted as CuPb$_9$(PO$_4$)$_6$OH$_2$, could be a room-temperature superconductor have led to an intense research activity. While other research groups did not confirm these claims, and the hope of realizing superconductivity in this compound has all but vanished, other findings have emerged which motivate further work on this material. In fact, Density Functional Theory (DFT) calculations indicate the presence of two nearly flat bands near the Fermi level, which are known to host strongly correlated physics. In order to facilitate the theoretical study of the intriguing physics associated with these two flat bands, we propose a minimal tight-binding model which reproduces their main features. We then calculate the orbital magnetic susceptibility of our two-band model and find a large diamagnetic response which arises due to the multi-orbital nature of the bands and which could provide an explanation for the strong diamagnetism reported in experiments.