Two-dimensional Dirac nodal line state protected against spin-orbit coupling in MoTe monolayer

We theoretically study a kind of protected double-nodal line state in two-dimensional (2D) transition metal monochalcogenide MoTe by using symmetry analysis and first-principles calculation. Among this kind of materials, there are various intriguing electronic properties, such as the long-range Coulomb interaction. The 2D layer four-fold degeneracy nodal line material is susceptible to the perturbation of strong spin-orbit coupling (SOC). We find that the Dirac degeneracy of two low-energy bands around the S point of the Brillouin zone is robust against SOC in P 2 1 / m -MoTe. The degeneracy nodal lines are protected by nonsymmorphic screw-rotational crystal symmetry and time-reversal symmetry. Due to the protection of symmetries, the Dirac double node line states under SOC are different from the accidental band touching. Furthermore, several isolog structures of P 2 1 / m -MoTe are also discussed. We find that the fourfold degeneracy nodal line state of MoSe also is robust against SOC, similar to MoTe. • DFT calculations and symmetry analysis confirm Dirac double-nodal line state in a stable 2D P21/m-MoTe. • The fourfold degeneracy nodal line robustness against SOC is protected by a combination of inversion, time reversal plus glide screw symmetries. • Another isolog structure P21/m-MoSe with longer Dirac double-nodal line state has been verified.