1.?

https://doi.org/10.48550/arXiv.2308.00676

摘要：A recent paper [Lee et al., J. Korean Cryt. Growth Cryst. Techn. 33, 61 (2023)] provides some experimental indications that Pb10?xCux(PO4)6O with x ≈ 1, coined LK-99, might be a roomtemperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with x – very similar to experiment. The DFT electronic structure shows Cu2+ in a 3d9 configuration with two extremely flat Cu bands crossing the Fermi energy. This puts Pb9Cu(PO4)6O in an ultracorrelated regime and suggests that, without doping, it is a Mott or charge transfer insulator. If doped such an electronic structure might support flat-band superconductivity or an correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.?

2.?

https://doi.org/10.48550/arXiv.2307.16040

摘要：Recently, Lee et al. reported the experimental discovery of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99) (arXiv:2307.12008, arXiv:2307.12037). Remarkably, the superconductivity persists up to 400 K at ambient pressure. Despite strong experimental evidence, the electronic structure of LK-99 has not yet been studied. Here, we investigate the electronic structures of LK-99 and its parent compound using first-principles calculations, aiming to elucidate the doping effects of Cu. Our results reveal that the parent compound Pb10(PO4)6O is an insulator, while Cu doping induces an insulator-metal transition and thus volume contraction. The band structures of LK-99 around the Fermi level are featured by a half-filled flat band and a fully-occupied flat band. These two flat bands arise from both the 2p orbitals of 1/4-occupied O atoms and the hybridization of the 3d orbitals of Cu with the 2p orbitals of its nearest-neighboring O atoms. Interestingly, we observe four van Hove singularities on these two flat bands. Furthermore, we show that the flat band structures can be tuned by including electronic correlation effects or by doping different elements. We find that among the considered doping elements (Ni, Cu, Zn, Ag, and Au), both Ni and Zn doping result in the gap opening, whereas Au exhibits doping effects more similar to Cu than Ag. Our work provides a foundation for future studies on the role of unique electronic structures of LK-99 in superconductivity.

3.?

https://doi.org/10.48550/arXiv.2307.16892

摘要：

A recent report of room temperature superconductivity at ambient pressure in Cu-substituted apatite (‘LK99’) has invigorated interest in the understanding of what materials and mechanisms can allow for high-temperature superconductivity. Here I perform density functional theory calculations on Cu-substituted lead phosphate apatite, identifying correlated isolated flat bands at the Fermi level, a common signature of high transition temperatures in already established families of superconductors. I elucidate the origins of these isolated bands as arising from a structural distortion induced by the Cu ions and a chiral charge density wave from the Pb lone pairs. These results suggest that a minimal two-band model can encompass much of the low-energy physics in this system. Finally, I discuss the implications of my results on possible superconductivity in Cu-doped apatite.

4.?

https://doi.org/10.48550/arXiv.2308.00698

摘要：

Here, based upon density functional theory (DFT) calculations, we present the basic electronic structure of CuPb9(PO4)6O (Cu-doped lead apatite), showing that the low energy (near-Fermi level) states are dominated by Cu-O hybrid states. The filling of these states is nominally d9, consistent with the standard Cu2+ valence state. We find these states to be unusually flat (~ 0.2 eV dispersion), giving a very high density of electronic states (DOS) at the Fermi level that we argue can be a host for novel electronic physics, including potentially room temperature superconductivity. The states are in general sensitive to symmetry-lowering gapping possibilities that would remove the spectral weight from EF, but could be protected from this by disorder/doping heterogeneity in a real material. Importantly, this disorder is expected to be less damaging to superconductivity. Further, we claim that the emergence of these flat bands should be due to weak wavefunction overlap between the orbitals on Cu and O sites, owing to to the directional character of the constituent orbitals. Therefore, finding an appropriate host structure for minimizing hybridization between Cu and O while allowing them to still weakly interact should be a promising route for generating flat bands at EF and very high temperature superconductivity, regardless of whether “LK-99” is such a realization.