Two-dimensional nonsymmorphic Dirac semimetal in chemically modified group-VA Monolayer with Black Phosphorene structure*

The symmetry-protected 2D Dirac semimetals have attracted intense interest due to their intriguing properties. Here, we investigate the 2D nonsymmorphic Dirac semimetal state by chemically modified group-VA 2D puckered structure. Based on first-principles calculations, we demonstrated 2D Dirac fermionic states not only exist, but in fact occur with two different types: one is a Dirac nodal line (DNL) structure in one-side modified phosphorene structure with negligible SOC; the other is a hourglass fermion protected by nonsymmorphic symmetry for the heavy elements with strong SOC. In the absence of SOC, the DNL exhibits anisotropic behavior and unique electronic properties, such as constant density of states. The Dirac node is protected from gap opening by nonsymmorphic symmetry. With the inclusion of SOC, the DNL states are split to form the hourglass dispersion due to broken inversion symmetry and Rashba SOC interaction. Moreover, around certain high symmetry points in the Brillouin zone, the spin orientation is enforced to be along a specific direction. The essential physics of 2D nonsymmorphic Dirac states is further analyzed by effective tight-binding models and group theory.