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 new and 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 eleven inequivalent nodal line Fermi surfaces together with their related constraints. By means of first-principles calculations, we first propose a family of real materials, beta phase of ternary nitrides X2GeN2 (X = Ca; Sr; Ba), that support one kind of these novel Fermi surfaces. Therefore, our work deepens the understanding of the nodal line structures and promotes the experimental progress of topological nodal line semimetals.
@article{arxiv.1804.06960,
title = {Mirror Protected Multiple Nodal Line Semimetals and Material Realization},
author = {Da-Shuai Ma and Jianhui Zhou and Botao Fu and Zhi-Ming Yu and Cheng-Cheng Liu and Yugui Yao},
journal= {arXiv preprint arXiv:1804.06960},
year = {2018}
}