  Using ab initio calculations based on density-functional theory and effective
model analysis, we propose that the trigonal YH3(Space Group: P-3c1) at ambient
pressure is a node-line semimetal when spin-orbit coupling (SOC) is ignored.
This trigonal YH3 has very clean electronic structure near Fermi level and its
nodal lines locate very closely to the Fermi energy, which makes it a perfect
system for model analysis. Symmetry analysis shows that the nodal ring in this
compound is protected by the glide-plane symmetry, where the band inversion of
|Y+,dxz> and |H1-,s> orbits at Gamma point is responsible for the formation of
the nodal lines. When SOC is included, the line nodes are prohibited by the
glide-plane symmetry, and a small gap (~5 meV) appears, which leads YH3 to be a
strong topological insulator with Z2 indices (1,000). Thus the glide-plane
symmetry plays an opposite role in the formation of the nodal lines in cases
without and with SOC. As the SOC-induced gap is so small that can be neglected,
this P-3c1 YH3 may be a good candidate for experimental explorations on the
fundamental physics of topological node-line semimetals. We find the surface
states of this P-3c1 phase are somehow unique and may be helpful to identify
the real ground state of YH3 in the experiment.
