Encyclopedia of emergent particles in 529 magnetic layer groups and 394 magnetic rod groups

Low dimensional crystals, including quasi-two-dimensional (2D) layered crystals and quasi-one-dimensional (1D) rod-like crystals, exhibit different properties from conventional three-dimensional crystals. In this work, we systematically study the emergent particles in 529 magnetic layer groups (MLGs) and 394 magnetic rod groups (MRGs). Based on restricting the co-representations of the magnetic space group to a subgroup, we construct the k·p Hamiltonians and identify all possible emergent particles, including spinful and spinless, essential, and accidental particles in 529 MLGs and 394 MRGs. We find that there are six kinds of emergent particles in MLGs and three kinds of emergent particles in MRGs. Moreover, we show the correspondence between MLGs (MRGs) and magnetic space groups. We hope this work will facilitate search and design low dimensional materials.