[Paper Review] Magnetic Properties and Spin-orbit Coupling induced Semiconductivity in LK-99

Hua Bai, Lei Gao+3 more|arXiv (Cornell University)|Aug 9, 2023

Crystal Structures and Properties4 citations

TL;DR

This study demonstrates that spin-orbit coupling (SOC) transforms Pb9Cu(PO4)6O (LK-99) from a predicted flat-band metal into a magnetic semiconductor, resolving discrepancies between prior SOC-ignored first-principles calculations and experimental observations. With SOC, the material becomes an indirect-bandgap semiconductor (292 meV) in the ferromagnetic state and a direct-bandgap semiconductor (300 meV) in the antiferromagnetic-A state, with a narrow flat band (25 meV width) at the Fermi level upon electron doping.

ABSTRACT

Recent reports of a possible room-temperature superconductor called LK-99 have generated a lot of attention worldwide. In just a few days, a large amount of experimental works attempted to reproduce this sample and verify its properties. At the same time a large amount of theoretical works have also been reported. However, many experiments have drawn different conclusions, and many theoretical results are not consistent with experimental results. For one of the structures of LK-99 with the chemical formula as Pb9Cu(PO4)6O, many first-principles calculations did not consider spin-orbit coupling and concluded that it is a flat band metal. However, spin-orbit coupling is often not negligible in systems with heavy elements, and LK-99 contains a large amount of heavy element Pb. We performed calculations of electronic structure of Pb9Cu(PO4)6O with spin-orbit coupling, and the results show that it's not a metal but a semiconductor. This is consistent with many experimental results. In the ferromagnetic state Pb9Cu(PO4)6O is an indirect-bandgap semiconductor with a bandgap of 292 meV. Moreover, its conduction band is a flat band. At an electron doping level of 0.5 e/unit cell, Pb9Cu(PO4)6O becomes metallic and has a flat band with a width of only 25 meV at the Fermi level in the ferromagnetic state. While in the antiferromagnetic-A state, Pb9Cu(PO4)6O is a direct-bandgap semiconductor with a bandgap of 300 meV. As a magnetic narrowband semiconductor, Pb9Cu(PO4)6O may have potential application value in the field of optoelectronic device, photocatalytic, photodetector and spintronics device.

Motivation & Objective

• To resolve inconsistencies between prior first-principles calculations (ignoring spin-orbit coupling) and experimental observations of LK-99's electronic properties.
• To investigate the role of spin-orbit coupling in Pb9Cu(PO4)6O, a key component of LK-99, given the presence of heavy Pb atoms.
• To determine the electronic structure and magnetic ground state of LK-99 with and without spin-orbit coupling.
• To explore the impact of electron doping on the electronic properties, particularly the formation of flat bands at the Fermi level.

Proposed method

• Performed first-principles density functional theory (DFT) calculations with the Hubbard U correction (U = 4 eV) for electronic structure analysis.
• Included spin-orbit coupling (SOC) in calculations to assess its effect on band dispersion and bandgap opening.
• Analyzed multiple magnetic configurations: ferromagnetic (FM), antiferromagnetic-A (AFM-A), AFM-C, and AFM-G, using a 2×2×2 supercell.
• Computed projected density of states (PDOS) to identify orbital contributions to electronic states.
• Evaluated the effect of electron doping (0.5 e/unit cell) on the Fermi-level electronic structure.
• Compared total energies of different magnetic states to determine the ground state, with SOC and U corrections.

Experimental results

Research questions

• RQ1 Does including spin-orbit coupling in first-principles calculations change the predicted metallic nature of LK-99 into a semiconductor?
• RQ2 What is the magnetic ground state of Pb9Cu(PO4)6O when spin-orbit coupling is included?
• RQ3 How does electron doping affect the formation of flat bands at the Fermi level in the ferromagnetic state of LK-99?
• RQ4 What is the bandgap size and type (direct/indirect) in the antiferromagnetic-A state of LK-99 with spin-orbit coupling?
• RQ5 How do the electronic properties of LK-99 differ when spin-orbit coupling is neglected versus included?

Key findings

• Including spin-orbit coupling transforms Pb9Cu(PO4)6O from a predicted flat-band metal into an indirect-bandgap semiconductor with a 292 meV bandgap in the ferromagnetic state.
• In the antiferromagnetic-A state, the material is a direct-bandgap semiconductor with a 300 meV bandgap.
• The conduction band in the ferromagnetic state is a flat band, and upon electron doping of 0.5 e/unit cell, it becomes metallic with a very narrow flat band width of only 25 meV at the Fermi level.
• The ground state of LK-99 is the antiferromagnetic-A state, with a small energy difference between magnetic configurations, indicating magnetic instability.
• The inclusion of spin-orbit coupling induces band inversion in the flat bands, leading to a significant bandgap opening that reconciles theoretical predictions with experimental observations.
• The material exhibits a magnetic moment of approximately 1 μB, with the easy axis of magnetization along the c-axis.