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

Abstract

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