As a type of fermions without counterpart in high energy physics, triply degenerate fermions show exotic physical properties, which are represented by triply degenerate nodal points in topological semimetals. Here, based on the space group theory analysis, we propose a practical guidance for seeking a topological semimetal with triply degenerate nodal points located at a symmetric axis, which is applicable to both symmorphic and nonsymmorphic crystals. By using this guidance in combination with the first-principles electronic structure calculations, we predict a class of triply degenerate topological semimetals $R{\mathrm{Rh}}_6{\mathrm{Ge}}_4(R=\text{Y},\text{La},\text{Lu})$. In these compounds, the triply degenerate nodal points are located at the $\mathrm{\Gamma }\text{−}A$ axis and not far from the Fermi level. Especially, ${\mathrm{LaRh}}_6{\mathrm{Ge}}_4$ has a pair of triply degenerate nodal points located at just $\sim 3$ meV below the Fermi level. Considering the fact that the single crystals of $R{\mathrm{Rh}}_6{\mathrm{Ge}}_4$ have been synthesized experimentally, the $R{\mathrm{Rh}}_6{\mathrm{Ge}}_4$ class of compounds will be an appropriate platform for studying exotic physical properties of triply degenerate topological semimetals.

• Received 11 November 2017

DOI:https://doi.org/10.1103/PhysRevB.98.045134