Minimal Model for the Flat Bands in Copper-substituted Lead Phosphate Apatite

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Discussion— In conclusion, two canadian researhcers have proposed a minimal two-band model which reproduces the main features of the Cu dzx and dzy flat bands predicted to appear in a copper-substituted lead apatite. They hope the model facilitates the investigation of the fascinating strongly correlated physics which could be hosted by these bands. As a first step in that direction, they have already discussed the only possible on-site superconducting order parameter allowed by their model, which is in the f-wave channel.

Their model was intended to be minimal and could be improved in a number of ways. The most pressing aspect is probably the fact that the DFT prediction gives a bottom band which is actually not perfectly dispersionless in the plane, especially close to the H point. Making the bottom band slightly dispersive could be achieved by adding longer-range hopping, which would destroy the existence of perfectly localized states. In their discussion of superconductivity, they have assumed that only the top band contributes. While this is true at kz = 0, the bottom band gets very close to the Fermi level at kz = π and could thus become important there. More generally, the question of whether the bottom band and three-dimensional effects can be neglected when studying superconductivity will have to be addressed.

Omid Tavakol1, 2 and Thomas Scaffidi1, 2
1Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
2Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 1A7, Canada
(Dated: August 3, 2023)

Abstract

Two recent preprints gave evidence that a copper-substituted lead apatite, denoted as CuPb9(PO4)6OH2 and also known as LK99, could be a room-temperature superconductor. While other research groups have not yet replicated the superconductivity in this material, a recent Density Functional Theory (DFT) calculation indicated the presence of two nearly flat bands near the Fermi level. Such flat bands are known to exhibit strongly correlated physics, which could potentially explain the reported high-Tc superconductivity. 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 also discuss implications for superconductivity.