Cubic Dirac Semimetals and Applications to Rare-Earth Magnets

Magnetic topological semimetals with cubic symmetric parent states, particularly those in rare-earth monopnictides, have attracted significant interest due to their complex topological properties. Although Dirac crossings can emerge from these symmetries, their influence on electronic behavior in these systems is not understood. Here, we develop minimal models for Dirac Semimetals (DSMs) with higher-order topology in cubic systems, incorporating magnetic orders and space group symmetries to investigate bulk, surface and hinge state properties. Our calculations reveal key features in the surface state dispersions, Fermi arcs, polarization dependence, and band splitting, which align with experimental findings. We also propose further tests and potential candidate materials for experimental validation. These results suggest that DSM physics may provide crucial hints toward understanding surface states in rare-earth monopnictides and their underlying topological origins.