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We study a class of topological materials which in their momentum-space band structure exhibit three-fold degeneracies known as triple points. Specifically, we investigate and classify triple points occurring along high-symmetry lines of $\mathcal{P}\mathcal{T}$-symmetric crystalline solids with negligible spin-orbit coupling. By employing the recently discovered non-Abelian band topology, we argue that a rotation-symmetry-breaking strain transforms a certain class of triple points into multi-band nodal links. Although multi-band nodal-line compositions were previously theoretically conceived, a practical condensed-matter platform for their manipulation and inspection has hitherto been missing. By reviewing the known triple-point materials in the considered symmetry class, and by performing first-principles calculations to predict new ones, we identify suitable candidates for the realization of multi-band nodal links. In particular, we find that Li$_2$NaN is an ideal compound to study this phenomenon, where the band nodes facilitate largely tunable density of states and optical conductivity with doping and strain, respectively. The multi-band linking is expected to equip the nodal rings with monopole charges, making such triple-point materials a versatile platform to probe the non-Abelian band topology.

Data and code for: Multi-band nodal links in triple-point materials