Topological nodal line semimetals with and without spin-orbital coupling

TLDR

Nodal‑line semimetals differ from point‑node TSMs such as Weyl and Dirac semimetals by exhibiting band crossings along closed loops in the Brillouin zone. The study theoretically investigates 3D topological semimetals with nodal lines protected by crystalline symmetries and proposes two new classes of symmetry‑protected nodal lines, one without and one with spin‑orbit coupling. The authors introduce two symmetry‑protected nodal‑line classes: one without SOC, where inversion and time‑reversal symmetry yield $Z_2$‑charged nodal lines that appear or disappear in pairs, and one with SOC, where a nonsymmorphic screw axis protects a four‑band crossing nodal line in systems with inversion and time‑reversal symmetry. The study finds that nodal lines without SOC possess a $Z_2$ monopole charge and must be created or annihilated in pairs, while nodal lines with SOC are protected by a nonsymmorphic screw axis and form four‑band crossing loops in systems with inversion and time‑reversal symmetry.

Abstract

We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared with TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these new TSMs the two bands cross at closed lines in the Brillouin zone. We propose two new classes of symmetry protected nodal lines in the absence and in the presence of spin-orbital coupling (SOC), respectively. In the former, we discuss nodal lines that are protected by the combination of inversion symmetry and time-reversal symmetry; yet unlike any previously studied nodal lines in the same symmetry class, each nodal line has a $Z_2$ monopole charge and can only be created (annihilated) in pairs. In the second class, with SOC, we show that a nonsymmorphic symmetry (screw axis) protects a four-band crossing nodal line in systems having both inversion and time-reversal symmetries.