Topological nodal line semimetals with and without spin-orbital coupling

TL;DR

This paper theoretically explores new classes of three-dimensional topological semimetals with nodal lines protected by crystalline symmetries, highlighting their unique properties with and without spin-orbital coupling.

Contribution

It introduces two novel classes of symmetry-protected nodal lines, one with $Z_2$ monopole charge and another protected by nonsymmorphic symmetry with SOC.

Findings

Nodal lines can have a $Z_2$ monopole charge and are created in pairs.

A nonsymmorphic symmetry protects a four-band crossing nodal line with SOC.

Different symmetry protections lead to distinct topological features.

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.