Cubic Dirac semimetals: General theory and application to rare-earth magnets

Rare-earth magnets with parent cubic symmetry exhibit unique topological properties. However, the origin of these behaviors presently remains unclear. Here, we develop minimal models for Dirac semimetals (DSMs) with accidental band crossings and higher-order topology in cubic systems, incorporating candidate magnetic order to analyze bulk, surface, and hinge state characteristics. In certain cubic-symmetric DSMs, we identify an effective <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn></a:msub></a:math> chiral symmetry which significantly impacts surface and hinge-localized states. Our results highlight distinct features in surface-state dispersions, Fermi arcs, polarization dependence, and band splitting that correlate with photoemission data in rare-earth monopnictides. We also suggest candidate materials and experimental tests for further validation. These findings advance our understanding of surface states in rare-earth magnets with parent cubic symmetries and illuminate the role of DSM physics in these systems.