Crystal Structures, Electronic Structures, and Topological Signatures in Equiatomic TT′X Compounds (T = Sc, Zr, Hf; T′ = Co, Pt, Pd, Ir, Rh; X = Al, Ga, Sn)

Here, based on first-principles calculations, we have made a systematical study on the crystal structures, electronic structures, topological signatures, and spin–orbit coupling (SOC) effects in a family of equiatomic TT′X compounds (T = Sc, Zr, Hf; T′ = Co, Pt, Pd, Ir, Rh; X = Al, Ga, Sn). The TT′X compounds all crystallize in the hexagonal ZrNiAl-type structure and exhibit metallic electronic structures. Very interestingly, we find their electronic structures all exhibit band crossings near the Fermi level, which are strong signatures for topological semimetals. By using ScSnPt as an example, we find that, it exhibits two pairs of triply degenerate nodal points (TDNPs), a nodal cage, and a nodal ring near the Fermi level when SOC is not considered. When SOC is taken into account, the strong band splitting in ScSnPt produces even more types of band crossings including three pairs of Weyl points in the Γ–A path, two Weyl nodal lines and two pairs of Weyl points in the k z = π plane, and three Weyl nodal rings and three TDNPs in the k x = π plane. In addition, the Weyl points, TDNPs, and nodal rings in ScSnPt show both type-I and type-II band dispersions. These results indicate that these TT′X compounds are excellent candidates to study the novel properties of Weyl, TDNP, and nodal ring Fermions, as well as the potential entanglements among these Fermionic states.