[Paper Review] First-principles calculation on the electronic structures, phonon dynamics, and electrical conductivities of Pb$_{10}$(PO$_4$)$_6$O and Pb$_9$Cu(PO$_4$)$_6$O compounds

Liyu Hao, Engang Fu|arXiv (Cornell University)|Aug 10, 2023

Geochemistry and Geologic MappingComputer Science3 citations

TL;DR

This first-principles study investigates the electronic, phononic, and electrical transport properties of Pb₁₀(PO₄)₆O and Pb₉Cu(PO₄)₆O, identifying the latter as a half-metal with spin-polarized conduction and anomalous conductivity enhancement above 400 K along the c-axis, while both compounds exhibit dynamic instability via negative phonon modes, challenging their experimental realization despite claims of high-Tc superconductivity in LK-99.

ABSTRACT

Superconducting materials with high critical temperature have the potential to revolutionize many fields, including military, electronic communications, and power energy. Therefore, Scientists around the world have been tirelessly working with the ultimate goal of achieving high temperature superconductivity. In 2023, a preprint by S. Lee et al in South Korea claimed the discovery of ultra-high-temperature superconductivity with a critical temperature of up to 423 K in Cu-doped lead-apatite (LK-99) (arXiv:2307.12008, arXiv:2307.12037), which caused a worldwide sensation and attention. Herein, the electronic structures, phonon dynamics, and electrical conductivities of LK-99 and its parent compound lead-apatite have been calculated using first-principles methods. The results show that the lead-apatite compound and the LK-99 compound are insulator and half-metal respectively. The flat band characteristic is consistent with previous calculations. The electrical conductivity of LK-99 compound shows two extreme point, and the electrical conductivity along the C-axis increases significantly after 400 K. The phonon dispersion spectra of the compounds were investigated, demonstrating their dynamic instability.

Motivation & Objective

• To evaluate the electronic structure and electrical conductivity of Pb₁₀(PO₄)₆O and Pb₉Cu(PO₄)₆O using first-principles methods.
• To investigate the potential for high-temperature superconductivity in LK-99 (Pb₉Cu(PO₄)₆O) based on its electronic and transport properties.
• To assess the dynamic stability of both compounds through phonon dispersion calculations.
• To resolve discrepancies in reported superconducting behavior by analyzing electronic and vibrational properties.
• To provide theoretical guidance for experimental synthesis of Pb₉Cu(PO₄)₆O, given its reported but unverified superconductivity.

Proposed method

• First-principles calculations were performed using the projector-augmented wave (PAW) method within the VASP package.
• The generalized gradient approximation (GGA-PBE) functional was used to describe electron exchange-correlation effects.
• A 3×3×3 Monkhorst-Pack k-mesh and 520 eV plane-wave cutoff were employed for convergence in electronic structure calculations.
• Spin-polarized calculations were applied to Pb₉Cu(PO₄)₆O to account for Cu 3d magnetic moments, while spin-unpolarized calculations were used for Pb₁₀(PO₄)₆O.
• Electrical conductivity was computed using the generalized Drude model via the BoltzTraP2 package, with temperature-dependent analysis.
• Phonon dispersion relations were calculated using the finite displacement method to assess dynamic stability.

Experimental results

Research questions

• RQ1 Is Pb₉Cu(PO₄)₆O (LK-99) electronically metallic or insulating, and does it exhibit half-metallic character?
• RQ2 How does the electrical conductivity of Pb₉Cu(PO₄)₆O vary with temperature, particularly along the c-axis?
• RQ3 What is the role of flat bands near the Fermi level in the electronic response of these compounds?
• RQ4 Are the Pb₁₀(PO₄)₆O and Pb₉Cu(PO₄)₆O structures dynamically stable, as indicated by phonon dispersion spectra?
• RQ5 Can the reported superconductivity in LK-99 be supported by first-principles electronic and vibrational properties?

Key findings

• Pb₁₀(PO₄)₆O is a band insulator with a band gap consistent with previous calculations, showing no metallic character.
• Pb₉Cu(PO₄)₆O exhibits half-metallic behavior: metallic for spin-up electrons and insulating for spin-down electrons, with two half-filled flat bands at the Fermi level due to O-2p and Cu-3d orbital hybridization.
• Electrical conductivity of Pb₉Cu(PO₄)₆O shows two distinct peaks and a sharp increase along the c-axis above 400 K, suggesting one-dimensional conduction channels involving 1/4-occupied O atoms and Cu/Pb chains.
• The generalized conductivity of Pb₉Cu(PO₄)₆O is 3–4 orders of magnitude lower than that of typical metals, making high-Tc superconductivity unlikely based on transport alone.
• Phonon dispersion spectra reveal negative modes in both compounds, indicating dynamic instability; Pb₉Cu(PO₄)₆O shows two modes below -2 THz, suggesting strong lattice anharmonicity.
• The dynamic instability implies that Pb₉Cu(PO₄)₆O is not a stable equilibrium phase and may only form under non-equilibrium conditions or at small scales, complicating experimental verification.