Cubic ScPd topological metal: Closed nodal line, spin-orbit coupling-induced triply degenerate nodal point–Dirac nodal point transition

Abstract

The presence of nodal points (NPs) and nodal lines (NLs) in the momentum space of topological materials is accompanied by many interesting properties. In this study, we predicted that an existing material ScPd with Pm3¯m-type structure would have closed NLs in the kx/y/z = 0 planes and one pair of triply degenerate NPs (TNPs) along the R-M-R′ paths, respectively, when the spin–orbit coupling (SOC) effect is not taken into consideration. Obvious nontrivial surface states were found around band-crossing points A, B, and C, which can be seen as good evidence for the topological signatures of ScPd metal. When the SOC effect was added, a TNP–Dirac NP (DNP) transition appeared along the R-M-R′ paths. Also, the band-crossing points belonging to the closed NL in the kx/y/z = 0 planes were gapped by the induction of SOC. However, the SOC-induced gaps were very small (<30 meV), and their values were much smaller than those of some well-studied nodal-line materials. The [001] surface states of ScPd under the SOC effect were also determined, showing that the nontrivial surface state was maintained near the newly occurring topological signature, i.e., DNP. Remarkably, a type I surface Dirac-like crossing was found at the X¯ point. This material has been proved to be dynamically and mechanically stable in theory and has been synthesized experimentally; it is therefore a good target for future investigation of the properties of NLs and NPs, and their relationship.