[Paper Review] Origin of correlated isolated flat bands in copper-substituted lead phosphate apatite

Sinéad M. Griffin|arXiv (Cornell University)|Jul 31, 2023

Iron-based superconductors research30 citations

TL;DR

The paper uses DFT with Hubbard U to show that Cu substitution in lead phosphate apatite creates an isolated, flat Cu-dominated band at the Fermi level, driven by Cu-induced structural distortion and Pb lone-pair–driven chiral charge density waves, suggesting a minimal two-band model for low-energy physics and potential superconductivity.

ABSTRACT

A recent report of room temperature superconductivity at ambient pressure in Cu-substituted apatite (`LK99') has invigorated interest in the understanding of what materials and mechanisms can allow for high-temperature superconductivity. Here I perform density functional theory calculations on Cu-substituted lead phosphate apatite, identifying correlated isolated flat bands at the Fermi level, a common signature of high transition temperatures in already established families of superconductors. I elucidate the origins of these isolated bands as arising from a structural distortion induced by the Cu ions and a chiral charge density wave from the Pb lone pairs. These results suggest that a minimal two-band model can encompass much of the low-energy physics in this system. Finally, I discuss the implications of my results on possible superconductivity in Cu-doped apatite.

Motivation & Objective

• Understand the structural and electronic origin of correlated flat bands in Cu-doped lead phosphate apatite.
• Identify how Cu substitution alters local coordination and polyhedral tilts.
• Assess implications for low-energy models and potential superconductivity in Cu-doped apatite.

Proposed method

• Perform density functional theory calculations with VASP.
• Apply GGA+U (Cu-d states) with U values 2–6 eV; main results use U=4 eV.
• Include spin-orbit coupling; analyze electronic structure and projected DOS.
• Relax structures to capture Cu-induced distortions and compute symmetry-adapted phonon modes with AMPLIMODES.
• Compare Cu substitution on Pb(1) versus Pb(2) sites and test non-relaxed structures to assess robustness.

Figure 1: (a) Lead-phosphate apatite structure with two inequivalent Pb sites as described in the main text. Columns of O or OH sit in the center column defined by Pb(2) hexagonal structure. (b) Calculated electronic localization function for Pb 10 (PO 4 ) 6 OH 2 . Oxygens surrounding Pb(2) are repe

Experimental results

Research questions

• RQ1 What structural distortions does Cu substitution induce in Pb10(PO4)6(OH)2 apatite?
• RQ2 How does Cu substitution affect the Cu-d derived bands and their isolation at the Fermi level?
• RQ3 Can a minimal two-band model (d_yz/d_xz) describe the low-energy physics of Cu-doped apatite?
• RQ4 What are the potential competing interactions (magnetic, charge, phonons) relevant to superconductivity in this system?

Key findings

• Cu substitution on the Pb(1) site yields an isolated pair of flat Cu-d bands crossing the Fermi level with bandwidth ~130 meV.
• These flat bands are separated from the rest of the valence manifold by ~160 meV, indicating strong correlation potential.
• Cu-induced distortion changes Cu coordination from ninefold to sixfold, forming a Jahn-Teller distorted trigonal prism that contributes to the flat-band formation.
• Pb(2) lone pairs create a chiral charge density wave that drives a structural distortion propagating via PO4 polyhedra; this lone-pair activity is linked to the electronic structure.
• A two-band model focusing on Cu-d_yz/d_xz states can capture the low-energy physics, with spin polarization and modest U dependence preserving the flat-band feature.
• Out-of-plane Cu-Cu exchange is FM by ~2 meV per Cu, while in-plane coupling is AFM by ~7 μeV per Cu, under the assumption of Cu occupying the Pb(1) site.

Figure 2: (a) Lead-phosphate apatite structure showing nine-coordinated Pb(1) sites. (b) Cu-substituted structure showing six-coordinated Cu and Pb(1) sites with distorted trigonal prism coordination with two different bondlengths are a rigid twist of $\approx 24^{\circ}$ between the upper and lower