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 group, 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.

7 pages, 2 figures, 4 tables

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• Controllable Weyl Nodes and Fermi Arcs from Floquet Engineering Triple Fermions
• Electronic structures near unmovable nodal points and lines in two-dimensional materials
• Existence of Mexican-hat dispersion and symmetry group of a layer
• Movable but unavoidable nodal lines through high-symmetry points in two-dimensional materials