Coexistence of type-I and critical-type nodal line states in intermetallic compounds ScM (M = Cu, Ag, Au)

In recent years, topological semimetals such as Weyl, Dirac, and nodal-line semimetals have been a hot topic in the field of condensed matter physics. Depending on the orientation of band crossing in momentum space, topological semimetals and metals can be identified as type-I or type-II. Here, we report the coexistence of two new types of topological metal phase in the ScM (M = Cu, Ag, Au) intermetallic compounds (IMCs): (1) multi-nodal-lines semimetals (above Fermi energy), (2) critical-type nodal-lines (lower than Fermi energy). The first case has already been investigated. So, in this paper, we focus on the second case. We find that these IMCs can be an existing topological metal lower than Fermi energy, which are characterized with type-I (for ScCu and ScAu) and critical-type (for ScAg) nodal-lines in the bulk and drumhead liked surface states in the absence of the spin-orbit coupling (SOC). It has also been shown that when SOC is included, these compounds are converted into topological metal materials.