Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators

Topological crystalline insulators (TCIs) can host surface states whose anomalous band structure inherits the characteristics of the crystalline symmetry that protects the bulk topology. Especially, in magnetic crystals, the diversity of magnetic crystalline symmetries indicates the potential to achieve novel magnetic TCIs with distinct surface characteristics. Here, we propose a new type of magnetic TCI, coined the topological magnetic Dirac insulator (TMDI), whose two-dimensional (2D) surface hosts fourfold-degenerate Dirac fermions protected by either p'_c4mm or p4'g'm magnetic wallpaper groups (MWGs). The bulk band topology of TMDIs is protected by diagonal mirror symmetries, which give the chiral dispersion of surface Dirac fermions and mirror-protected hinge modes. We also propose a class of candidate materials for TMDIs including Nd₄Te₈Cl₄O₂₀ and DyB₄ based on first-principle calculations, and construct a general scheme to search TMDIs using the space group symmetry of paramagnetic parent states. We believe that our theoretical discovery of TMDIs and their anomalous surface Dirac fermions would facilitate the future research of new magnetic TCIs and illustrate a distinct way to achieve anomalous surface states in magnetic crystals.