Nonsymmorphic symmetry protected node-line semimetal in the trigonal YH₃

Using ab initio calculations based on density-functional theory and effective model analysis, we propose that the trigonal YH₃ (Space Group: P[Formula: see text]c1) 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⁺, d _xz 〉 and |H1^-, s〉 orbits at Γ 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[Formula: see text]c1 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[Formula: see text]c1 phase are somehow unique and may be helpful to identify the real ground state of YH₃ in the experiment.