Semiconductivity induced by spin-orbit coupling in Pb₉Cu(PO₄)₆O

Recently, a possible room-temperature superconductor known as LK-99 (Pb_10-xCu_x(PO₄)₆O (0.9 < x < 1.1)) has sparked a wave of research. However, many experimental works have proven that it is a semiconductor. At the same time, many theoretical works have reached the conclusion that it is a flat band metal. The inconsistency between theoretical and experimental works may be caused by neglecting the spin-orbit coupling effect in calculations. We performed calculations of electronic structure of Pb₉Cu(PO₄)₆O with spin-orbit coupling, and the results show that it's indeed a semiconductor, not a metal. In the ferromagnetic state it is an indirect-bandgap semiconductor with a bandgap of 292 meV. While in the antiferromagnetic-A state, it is a direct-bandgap semiconductor with a bandgap of 300 meV. Our work provides a possible explanation for the contradictions of previous experiments and theories, and provides some theoretical basis for the potential application of Pb₉Cu(PO₄)₆O as a semiconductor.