First-principles study on the electronic structure of Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O ($x$=0, 1)

Abstract: 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 Pb$_{10}$(PO$_4$)$_6$O 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.

• The paper demonstrates that pristine Pb10(PO4)6O is an insulator with a clear band gap, while Cu doping transitions it to a metallic state.
• The study employs first-principles DFT calculations to reveal flat bands and van Hove singularities that may underpin novel superconducting mechanisms.
• The findings advocate for a two-band low-energy model, suggesting targeted doping can effectively tune superconducting properties.

Insightful Overview of "First-principles study on the electronic structure of Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O ($x$=0, 1)"

The paper "First-principles study on the electronic structure of Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O ($x$=0, 1)" explores the electronic characteristics of the lead-apatite and its derivative LK-99, utilizing first-principles density functional theory (DFT) calculations. The focus of this research lies in delineating the effects of Cu doping on the electronic structures, offering an insightful avenue to further understand the superconductivity exhibited by LK-99. This comprehensive study is pivotal as it offers mechanistic insights into the transition between insulating and metallic states induced by doping, a domain extensively explored in the physics of superconductors.

Main Findings

The DFT calculations reveal that the parent lead-apatite compound, Pb$_{10}$(PO$_4$)$_6$O, is an insulator, with a predicted band gap that aligns well with experimental observations. This insulating nature is attributed predominantly to the electronic structure contributions from O-$2p$ orbitals and stereochemically active $6s^2$ lone pairs on Pb atoms, which contribute to the presence of flat bands below the Fermi level. The introduction of Cu, replacing Pb, transitions the system into a metallic state, consistent with the experimentally observed room-temperature superconductivity of LK-99.

The electronic structure of LK-99 is particularly noted for its half-filled flat band around the Fermi level and the presence of notable van Hove singularities (VHSs). These features are critical as they suggest a pathway for electronic correlation effects which are central to superconductivity. The flat bands predominantly arise from hybridization between Cu-$3d$ orbitals and neighboring O-$2p$ orbitals, a characteristic that can be exploited to explore novel superconducting states.

Theoretical and Practical Implications

From a theoretical standpoint, the distinct electronic structure of LK-99, particularly its flat bands and VHSs, requires more detailed investigation to elucidate its contribution to high-temperature superconductivity. The observed electronic structures necessitate a minimum two-band model to adequately describe the materials’ low-energy physics, diverging from the conventional universal one-band models applied to cuprate superconductors.

Experimentally, the ability to tune electronic properties through doping, as demonstrated with various elements like Ni, Zn, Ag, and Au, provides a pathway to tailor superconductive properties or potentially discover new materials exhibiting room-temperature superconductivity.

Speculations on Future Developments

This study opens up several avenues for future research. The presence of VHSs emphasizes the possibility of exploring superconducting pairing mechanisms beyond those of conventional BCS theory. In combination with experimental efforts, theoretical advancements focusing on quantum many-body effects could be pivotal in developing an exhaustive understanding of the superconducting behavior in such complex materials.

Moreover, the findings suggest further exploration of doping effects which could lead to a controlled manipulation of electronic states to optimize superconducting characteristics. Additionally, advancing theoretical models that incorporate both electronic correlations and structural instabilities could illuminate unexplored regions in the superconducting phase space.

In summary, the paper provides a solid groundwork for exploring the electronic structures that underpin superconductivity in doped lead-apatite systems. Further advancements in both theoretical methodologies and experimental validations will be crucial to unraveling and harnessing the potential of these remarkable materials.