Higher-fold chiral fermions that go beyond twofold Weyl fermions have recently been reported in crystalline systems. Here, we focus on such excitations in several binary, ternary, and quaternary alloys/compounds with CoGe, BiSbPt, and ${\mathrm{KMgBO}}_3$ as the representative examples that belong to the crystal space group 198. We found distinct threefold, fourfold, and sixfold chiral fermions in the bulk via density-functional computations. We provide general symmetry arguments for the protection of these degeneracies with special emphasis on the fourfold fermions. Our surface spectra simulations show that the size of Fermi arcs resulting from these chiral fermions are large, robust, and untouched from the bulk states due to the near absence of trivial bulk Fermi pockets. All these features make these systems—especially CoGe and ${\mathrm{KMgBO}}_3$—promising topological semimetal candidates to realize higher-fold fermions in future photoemission and transport experiments.

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• Crystal symmetry
• Electronic structure
• Dirac semimetal
• Topological materials
• Ab initio calculations
• Band structure methods
• Density functional theory
• k dot p method