Mirror protected multiple nodal line semimetals and material realization

The conventional k·p method fails to capture the full and essential physics of many symmetry enriched multiple nodal line structures in the three-dimensional Brillouin zone. Here, we present a systematical method to construct the effective lattice model of mirror symmetry protected three-dimensional multiple nodal line semimetals, when the spin-orbit interaction is ignored. For systems with a given pair of perpendicular nodal rings, we obtain all the effective lattice models and 11 inequivalent nodal line Fermi surfaces together with their related constraints. By means of first-principles calculations, we first propose a family of real materials, the β phase of ternary nitrides X2GeN2 (X=Ca,Sr,Ba), that support one kind of these Fermi surfaces. Therefore, our work deepens the understanding of the nodal line structures and promotes the experimental progress of topological nodal line semimetals.