Symmetry-protected multiple-type nodal lines in intermetallic XY (X = Ca, Rare earth; Y = Ni, PGE, Ag, Cu)

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Nodal line semimetals (NLSMs) have been widely studied in condensed matter physics, due to interesting electronic behaviors and wide application in electronic devices. Generally, based on band dispersion, the linear nodal lines (NLs) can be classified into four types, namely type-I, type-II, critical-type, and hybrid-type. In particular, realistic critical-type NLs are relatively rare. Here, we systematically report a series of NLSMs (thirty-one NLSMs) with critical-type and type-I one-dimensional (1D) crossings, namely intermetallic XY (X = Ca, Rare earth; Y = Ni, PGE, Ag, Cu). Specifically, in Pm3̅m space group with the time (T) and spatial (P) reversal invariances, we find thirty-one synthesized NLSMs, which contain five critical-type NLSMs and twenty-six type-I NLSMs. It is worth noting that these non-trivial NLs show clear drumhead surface states. Also, these NLs are protected by PT and Mz symmetries, showing strong robustness. Besides, these NL fermions possess excellent regulation properties for band dispersion and energy level. Also, these NLs open tiny energy gaps (<100 meV) under SOC, very closing to previous typical NLSMs. The above results indicate we provide a number of excellent candidate materials for the future research on NL fermions and their potential applications in electronic devices.