[Paper Review] Effective model for Pb$_9$Cu(PO$_4$)$_6$O

Patrick A. Lee, Zhehao Dai|arXiv (Cornell University)|Aug 8, 2023

Physics of Superconductivity and Magnetism4 citations

TL;DR

The paper proposes an effective low-energy model for Pb9Cu(PO4)6O (LK-99) as a stack of buckled honeycomb lattices with Cu and O on A and B sites, emphasizing a charge-transfer mechanism with a small energy gap D ≈ 0.4 eV between Cu d and O p orbitals. Despite small hopping integrals (t ≈ 80 meV), the system may reside near a metal-insulator transition, enabling unconventional superconductivity in an intermediate correlation regime akin to organic superconductors, though with a low Tc due to small energy scales.

ABSTRACT

The copper substituted Pb-apatite has attracted a great deal of attention recently, due to the claim of the observation of room temperature superconductivity. Based on LDA calculations in the literature, we propose an effective model that describe the low energy physics. It consists of stacks of buckled honeycomb lattices, with Cu and O occupying the A and B sites respectively. In addition to the narrow Cu bands that have been emphasized, we call attention to the relatively small energy separation between the Cu and O orbitals. Thus despite the small hoping energies, the model may be in an interesting regime near the metal insulator transition driven by the charge transfer mechanism. Relationship with cuprates and the organic superconductors are discussed.

Motivation & Objective

• To identify the low-energy electronic degrees of freedom in Pb9Cu(PO4)6O (LK-99) based on LDA band structure calculations.
• To argue that the system may be in an intermediate correlation regime near a metal-insulator transition, despite small hopping integrals.
• To propose an effective Hamiltonian model with Cu and O orbitals on a buckled honeycomb lattice, capturing key physics near the charge-transfer insulator regime.
• To explore the potential for unconventional superconductivity in this system, drawing analogies to organic superconductors and cuprates.
• To highlight the importance of the small energy separation D ≈ 0.4 eV between Cu d and O p orbitals in enabling strong correlation effects.

Proposed method

• The effective model is constructed from LDA band structure results, focusing on the Cu d and O p bands near the Fermi level.
• The system is modeled as a stack of buckled honeycomb lattices with Cu on A sites and O on B sites, breaking inversion symmetry.
• The Hamiltonian includes nearest-neighbor hopping between Cu d and O p orbitals, with a site energy difference D ≈ 0.4 eV.
• Interlayer hopping between O p orbitals (t_c) is included, which tends to drive the system into a 3D metallic state.
• The model is analyzed in the context of charge-transfer physics, with D/t ≈ 5 suggesting proximity to the metal-insulator transition.
• Numerical exploration of the model is planned to investigate spin liquid and superconducting phases near the transition.

Figure 1: (a) Top view and (b) side view of the structure of Pb 9 Cu(PO 4 ) 6 O, also known as LK-99, leaving out the PO 4 (adapted from [ 6 ] ). Six Pb2 ions form two triangles rotated by 60 degrees and separated by $c/2$ within the unit cell. Oxygen occupies the center of the top triangle as shown

Experimental results

Research questions

• RQ1 Can the low-energy physics of Pb9Cu(PO4)6O be captured by a model with Cu and O on a buckled honeycomb lattice?
• RQ2 Is the system in an intermediate correlation regime near a metal-insulator transition despite small hopping integrals?
• RQ3 What is the role of the small energy gap D ≈ 0.4 eV between Cu d and O p orbitals in enabling strong correlation effects?
• RQ4 Could this system host unconventional superconductivity, and how does its behavior compare to cuprates and organic superconductors?
• RQ5 How does the interlayer hopping between O orbitals influence the stability of metallic and superconducting phases?

Key findings

• The Cu d bands near the Fermi level are exceptionally narrow, with a total bandwidth of ~0.15 eV, indicating small hopping integrals.
• The O p bands lie ~0.4 eV below the Cu d bands, creating a small charge-transfer gap D ≈ 0.4 eV, significantly smaller than in cuprates (D ≈ 2 eV).
• Despite small t, the ratio D/t ≈ 5 suggests the system may be near the metal-insulator transition in a regime favorable to unconventional superconductivity.
• The effective model is a charge-transfer system on a buckled honeycomb lattice, with Cu on A sites and O on B sites, and includes interlayer hopping between O orbitals.
• The estimated hopping integral t ≈ 80 meV is of the same order of magnitude as in organic superconductors (e.g., 57 meV in κ-(BEDT-TTF)2Cu(CN)3), but the energy scale is much smaller than in cuprates.
• The system is unlikely to host high-Tc superconductivity due to small energy scales, but may exhibit exotic physics such as spin liquid or chiral superconductivity near the metal-insulator transition.