Topological materials have attracted immense research interest as a fertile ground for realizing exotic quasiparticles, such as Dirac/Weyl/Majorana fermions. Symmetry plays a vital role in classifying and diagnosing topological states of matter. Among the 230 space groups (SGs), 65 chiral SGs have been shown to enforce the existence of Weyl points at time-reversal invariant momenta through Kramers degeneracy in the electronic band structures of nonmagnetic materials with spin-orbit coupling (SOC). Current research on the correlation between topological quasiparticles and chiral crystal structures has mainly focused on nonmagnetic electronic systems, while studies on chiral phononic and magnetic materials remain scarce. In this work, we summarize the properties of topological quasiparticles at high-symmetry points and along high-symmetry lines in the 65 chiral SGs and their enantiomers, both with and without SOC. We also identify the achiral supergroups that share the same translational symmetry with the corresponding chiral SGs, providing guidance for realizing a chiral SG through symmetry breaking from an achiral supergroup. Using the nonmagnetic chiral materials ${\mathrm{Al}}_2{\mathrm{Nb}}_3\mathrm{N}$, ${\mathrm{Al}}_2{\mathrm{Nb}}_3\mathrm{C}$, and ${\mathrm{Al}}_2{\mathrm{Ta}}_3\mathrm{C}$ in SG 213, as well as the experimentally synthesized chiral collinear ferromagnet ${\mathrm{NaMnFeF}}_6$ in SG 150, as examples, we further reveal the correlation between structural chirality and quasiparticle chirality in both phononic and electronic systems. Our work provides a new platform for studying the manipulation of topological quasiparticles in chiral systems.

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• Phonons
• Ferromagnets
• Topological materials
• Chiral symmetry
• Density functional calculations
• k dot p method