Crossing-line-node semimetals: general theory and application to rare-earth trihydrides

Topological semimetals are phases of matter with the topological degeneracies near the Fermi level. The topological degeneracies appear as point nodes, line nodes, and surface nodes in the three-dimensional Brillouin zone, depending on the contact area between valence and conduction bands. In particular, line-node semimetals have great potential for realizing exotic electronic states.
In this work, we focus on crossing-line-node semimetals and study a general theory for it from the viewpoint of crystalline symmetry. The number of crossing line node is uniquely determined for a given level scheme in a given point group symmetry [1]. Taking into account the effect of spin-orbit interaction, we also clarify whether the resulting states are Dirac semimetal or topological insulator, which topological indices are determined for the level scheme and the number of line nodes encircling time-reversal invariant momentum [1].
As an example, we apply our theory to a hexagonal hydride YH₃, which hosts three crossing line nodes. A tiny energy gap is induced in the line nodes by spin-orbit interaction. The resulting state is a topological insulator with topological index (1;000).
[1] SK, Y. Yamakawa, A. Yamakage, T. Inohara, Y. Okamoto, and Y. Tanaka, Phys. Rev. B 95, 245208 (2017)