Pb-apatite framework as a generator of novel flat-band CuO based physics (2308.00698v2)

Abstract: Based on DFT calculations, we present the basic electronic structure of CuPb9(PO4)6O (Cu-doped lead apatite, LK-99), in two scenarios: (1) where the structure is constrained to the P3 symmetry and (2) where no symmetry is imposed. At the DFT level, the former is predicted to be metallic while the latter is found to be a charge-transfer insulator. In both cases the filling of these states is nominally d9, consistent with the Cu2+ valence state, and Cu with a local magnetic moment ~0.7mB. In the metallic case we find these states to be unusually flat (0.2 eV dispersion), giving high DOS at EF that we argue can be a host for novel electronic physics, including potentially high temperature superconductivity. The flatness of the bands is the likely origin of symmetry-lowering gapping possibilities that would remove the spectral weight from EF. Since some experimental observations show metallic/semiconducting behavior, we propose that disorder is responsible for closing the gap. We consider a variety of possibilities that could possibly close the gap, but limit consideration to kinds of disorder that preserve electron count. For all possibilities we considered (spin disorder, O on vacancy sites, Cu on different Pb sites), the local Cu moment, and consequently the gap remains robust. We conclude that disorder responsible for metallic behavior entails some kind of doping where the electron count changes. We claim that the emergence of the flat bands should be due to weak wave function overlap between the Cu and O orbitals, owing to the directional character of the constituent orbitals. So, 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 which can lead to interesting electronic phenomena, regardless of whether LK-99 is a room-temperature superconductor.

• The paper demonstrates that preserving P3 symmetry in Cu-doped Pb apatite produces metallic flat-band states with ~0.2 eV dispersion at the Fermi level.
• It employs density functional theory to analyze two structural variations, revealing Cu sites with a local magnetic moment of ~0.7 μB indicative of a Cu2+ state.
• The findings imply that controlling lattice symmetry and atomic disorder is crucial for leveraging flat-band phenomena in potential superconductivity applications.

Examination of Flat-Band Phenomena in Cu-Doped Lead Apatite Through Density Functional Theory

The paper explores the electronic properties of a Cu-doped lead apatite compound, CuPb$_9$(PO$_4$)$_6$O, commonly referred to as LK-99. The paper utilizes density functional theory (DFT) to uncover the full potential of this material in generating flat-band physics. This class of physics is noteworthy due to its propensity to offer intriguing electronic behaviors, potentially including high-temperature superconductivity.

The authors conduct the analysis on two structural variations of the material: one maintaining P3 symmetry and another without any symmetry constraint. They find the P3 symmetry-constrained structure presents a metallic character with unusually flat bands ($\sim$0.2 eV dispersion) manifesting at the Fermi level. Meanwhile, the symmetry-relaxed structure behaves as a charge-transfer insulator. In both cases, the Cu sites are characterized by a local magnetic moment of approximately 0.7 $\mu_B$, indicating a $d^9$ valence state akin to Cu$^{2+}$.

The results underline that maintaining P3 symmetry is crucial for the material to remain metallic, as symmetry-breaking introduces a substantial gap leading to an insulating state. This insight suggests that any electronic applications, such as superconductivity, will necessitate controls to preserve the material's structural symmetry—possibly through certain doping mechanisms that modify the electron count or by leveraging specific disorder types that resist electron transfer gap expansion.

The paper challenges the notion of LK-99 as a room-temperature superconductor but provides essential insights into the electronic configuration that may underpin novel superconducting behaviors. A notable feature is the high density of states at the Fermi level resulting from flat bands. Such conditions are favorable for electronic instabilities that often manifest as charge density waves or superconductivity, especially under high densities of states intrinsic to flat-band systems.

Experimentation with various atomic disorders, such as Cu replacement on Pb sites and variance in O occupancy, suggests robust local moments and a stable charge-transfer gap. This finding implies that while theoretical concepts of high-temperature superconductivity may seem compelling, practical realization in CuPb$_9$(PO$_4$)$_6$O hinges on sophisticated structuring and control over atomic disorders.

Overall, this paper provides a comprehensive investigation of the electronic structures arising from the interplay of lattice symmetry and electronic states in Cu-doped lead apatite. It establishes a significant footing for future exploration into flat-band systems that display implications for high-density electronic states, advancing the pursuit of viable superconductors guided by electronic structure optimization principles.

The implications of this work span from refining theoretical models that describe complex, itinerant electronic states in condensed matter systems to addressing practical challenges in stabilizing specific symmetric configurations of doped oxides. Future studies might investigate more about the additional doping strategies and the effect of external parameters, such as pressure or temperature, on these intricate electronic scenarios. Such research could open pathways to new materials that harness flat-band phenomena for emergent properties like superconductivity under ambient conditions. In sum, this paper lays the groundwork for future explorations in the design and synthesis of materials with exotic electronic and magnetic properties driven by flat bandwidths.