Topological nodal line semimetals with and without spin-orbital coupling

We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared to TSMs with point nodes, e. g. , Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these TSMs the two bands cross at closed lines in the Brillouin zone. We propose two different 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 a combination of inversion symmetry and time-reversal symmetry, yet, unlike previously studied nodal lines in the same symmetry class, each nodal line has a Z₂ 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.