Centrosymmetric, non-symmorphic, non-magnetic, spin–orbit coupled layers without Dirac cones

While considering the appearance of Dirac cones in spin–orbit coupled two-dimensional materials, Young and Kane (Phys Rev Lett 115:126803, 2015) have found that, in the absence of other symmetries, spatial-, time-reversal and vertical glide plane (or horizontal screw rotation) symmetry give four-fold degenerate Dirac point at the time-reversal invariant momentum along the fractional translation. Here we show in which cases additional symmetries lead to Dirac line instead of Dirac cone in the band structure. We found three centrosymmetric, non-symmorphic layer double groups with line-like degeneracies instead of nodal points. We show that besides these Dirac lines, no other band contacts occur, including the accidental ones. Our results are illustrated using a tight binding example arising from s-orbitals on two atoms in the primitive cell. Finally, we discussed ways towards realistic materials where such features in the electronic dispersion are expected to appear.