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The claims that a copper-substituted lead apatite, denoted asCuPb$_9$(PO$_4$)$_6$OH$_2$, could be a room-temperature superconductor have ledto an intense research activity. While other research groups did not confirmthese claims, and the hope of realizing superconductivity in this compound hasall but vanished, other findings have emerged which motivate further work onthis material. In fact, Density Functional Theory (DFT) calculations indicatethe presence of two nearly flat bands near the Fermi level, which are known tohost strongly correlated physics. In order to facilitate the theoretical studyof the intriguing physics associated with these two flat bands, we propose aminimal tight-binding model which reproduces their main features. We thencalculate the orbital magnetic susceptibility of our two-band model and find alarge diamagnetic response which arises due to the multi-orbital nature of thebands and which could provide an explanation for the strong diamagnetismreported in experiments.

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