Encyclopedia of emergent particles in type-IV magnetic space groups

TL;DR

This paper provides a comprehensive classification and an interactive resource for emergent particles in type-IV magnetic space groups, revealing new occurrences in spinful systems due to unique symmetry conditions.

Contribution

It offers the first complete classification of emergent particles in all 517 type-IV magnetic space groups, including detailed symmetry and topological information, with new insights into spinful system occurrences.

Findings

Emergent particles can occur in spinful systems due to type-IV MSG symmetries.

Interactive tables link particles to specific MSGs and their properties.

New conditions for stabilizing particles in magnetic systems are identified.

Abstract

The research on emergent particles in condensed matters has been attracting tremendous interest, and recently it is extended to magnetic systems. Here, we study the emergent particles stabilized by the symmetries of type-IV magnetic space groups (MSGs). Type-IV MSGs feature a special time reversal symmetry $\{\mathcal{T}|\boldsymbol{t}_0\}$, namely, the time reversal operation followed by a half lattice translation, which significantly alters the symmetry conditions for stabilizing the band degeneracies. In this work, based on symmetry analysis and modeling, we present a complete classification of emergent particles in type-IV MSGs by studying all possible (spinless and spinful, essential and accidental) particles in each of the 517 type-IV MSGs. Particularly, the detailed correspondence between the emergent particles and the type-IV MSGs that can host them are given in easily accessed interactive tables, where the basic information of the emergent particles, including the symmetry conditions, the effective Hamiltonian, the band dispersion and the topological characters can be found. According to the established encyclopedia, we find that several emergent particles that are previously believed to exist only in spinless systems will occur in spinful systems here, and vice versa, due to the $\{{\cal T}|\boldsymbol{t}_{0}\}$ symmetry. Our work not only deepens the understanding of the symmetry conditions for realizing emergent particles but also provides specific guidance for searching and designing materials with target particles.