Topological Nodal Lines from Crystalline Symmetry

Topological nodal lines protected by the time-reversal and space-inversion symmetry can be classified into two categories, depending on the value of the $Z_2$ monopole topological index. Nodal lines with trivial (non-trivial) monopole charge can (cannot) be gapped out via shrinking the nodal line into a point. In this study, we provide a general principle for finding topological nodal lines with nontrivial monopole charge based on the interplay between lattice crystalline symmetries and the time-reversal symmetry. In addition, this study also reveals a new family of topological nodal lines, protected by the time-reversal symmetry and point group symmetries.