Encyclopedia of emergent particles in 528 magnetic layer groups and 394 magnetic rod groups

We present a systematic classification of emergent particles in all 528 magnetic layer groups and 394 rod groups, which describe two-dimensional one-dimensional crystals respectively. Our approach is via constructing correspondence between given layer/rod group one the space group, such that irreducible representations can be derived from those corresponding group. Based on these representations, we explicitly construct effective models for possible band degeneracies identify particles, including both spinless spinful cases. find there are six kinds protected by three groups. work provides useful reference search design lower dimensional crystals.