We study the impact of spin-orbit coupling on the topological band-properties of copper-substituted lead phosphate apatite using a combination of group-theoretical analysis and full-relativistic density-functional theory calculations. We characterize Weyl points at time-reversal invariant momenta and find that a band-inversion due to spin-orbit coupling leads to additional Weyl points close to the Fermi-edge at general momenta. To determine the position of the altogether 66 Weyl points in the Brilouin-zone, we develop an algorithm that follows a Berry-curvature-derived vector field to its monopole: the Weyl point. The emerging surface Fermi-arcs and their spin-polarization reveal avoided crossings and a Fermi-loop detached from the Weyl points.
@article{arxiv.2310.09310,
title = {Weyl points and spin-orbit coupling in copper-substituted lead phosphate apatite},
author = {Martin Braß and Liang Si and Karten Held},
journal= {arXiv preprint arXiv:2310.09310},
year = {2023}
}