[Paper Review] Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O: a Mott or charge transfer insulator in need of further doping for (super)conductivity

Liang Si, Markus Wallerberger+4 more|arXiv (Cornell University)|Aug 8, 2023

Physics of Superconductivity and Magnetism10 citations

TL;DR

The paper analyzes LK-99, derives two- and five-band tight-binding models from ab initio data, and shows DMFT results indicating a Mott or charge-transfer insulator that requires electron or hole doping for metallicity and potential superconductivity.

ABSTRACT

We briefly review the status quo of research on the putative superconductor Pb$_9$Cu(PO$_4$)$_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from substituting Pb by Cu and thus differs from LK-99) is required to make it metallic and potentially superconducting.

Motivation & Objective

• Assess the electronic nature of Pb10-xCux(PO4)6O (LK-99) and clarify whether it is a Mott or charge-transfer insulator.
• Derive low-energy tight-binding models (two-band and five-band) from ab initio data.
• Investigate the role of electronic correlations via DMFT and determine the insulating state.
• Estimate realistic interaction parameters to discuss doping needed for metallicity or superconductivity.

Proposed method

• Perform DFT structural relaxations and band calculations to obtain a relaxed structure.
• Project DFT bands onto Wannier functions to obtain two-band and five-band tight-binding models.
• Add a local Kanamori interaction on Cu sites and solve with DMFT at 298 K using a continuous-time QMC solver.
• Compare DMFT spectra with DFT+U results to assess insulating behavior (Mott vs. charge-transfer).
• Use cRPA-inspired reasoning to discuss plausible U, J, and U' values for the models.

Figure 1: Top: Schematics of DFT bandstructure for Pb 9 Cu(PO 4 ) 6 O. Middle: Mott-Hubbard splitting of the Cu $d_{xz,yz}$ orbitals leading to a Mott or charge transfer insulator. Note here we visualize the case with an orbital symmetry breaking (ordering) indicating by having different orbitals in

Experimental results

Research questions

• RQ1 Is Pb10-xCux(PO4)6O a Mott or a charge-transfer insulator under realistic interaction strengths?
• RQ2 What are the low-energy electronic models (two-band and five-band) that best describe LK-99?
• RQ3 Does electronic correlation in DMFT open a gap, and how does the gap depend on U', J, and model choice?
• RQ4 What doping (electron or hole) is required to drive metallicity or superconductivity in this material?
• RQ5 How do DFT+U results compare with DMFT in capturing the insulating state and orbital polarization?

Key findings

• DMFT shows a clear gap at the Fermi energy with Cu d-band (d_xz/d_yz) split into lower and upper Hubbard bands.
• Five-band model indicates a charge-transfer insulator at U' = 3 eV and a Mott-like character at U' = 2 eV; the system is near a crossover between charge-transfer and Mott insulating behavior.
• Two-band model yields larger gaps due to less screening; orbitals remain degenerate without symmetry breaking in DMFT.
• DFT+U can yield an insulating state under symmetry-broken structures, highlighting the role of lattice distortions in stabilizing insulating behavior.
• Overall, LK-99 is predicted to be an insulator (Mott or charge-transfer) at moderate U; metallicity and possible superconductivity would require electron or hole doping beyond Cu Pb substitution.

Figure 2: (a) DFT-relaxed structure of Pb 9 Cu(PO 4 ) 6 O; (b) schematic figure of energy band splitting from the octahedral Cu-coordination of the CuO 6 motif; Wannier projections for the two bands model (c) and five bands model (d), respectively. The Wannier bands (dots) are virtually identical to