A 2D nonsymmorphic Dirac semimetal in a chemically modified group-VA monolayer with a black phosphorene structure

Abstract

A symmetry-protected 2D Dirac semimetal has attracted intense interest for its intriguing material properties. Here, we report a 2D nonsymmorphic Dirac semimetal state in a chemically modified group-VA 2D puckered structure. Based on first-principles calculations, we demonstrate the existence of 2D Dirac fermions in a one-side modified phosphorene structure in two different types: one with a Dirac nodal line (DNL) structure for light elements with negligible spin–orbit coupling (SOC) and the other having an hourglass band protected by a nonsymmorphic symmetry for heavy elements with strong SOC. In the absence of SOC, the DNL exhibits an anisotropic behavior and unique electronic properties, such as constant density of states. The Dirac node is protected from gap opening by the nonsymmorphic space group symmetry. In the presence of SOC, the DNL states split and form an hourglass-shaped dispersion due to the broken inversion symmetry and the Rashba SOC interaction. Moreover, around certain high symmetry points in the Brillouin zone, the spin orientation is enforced to be along a specific direction. We construct an effective tight-binding model to characterize the 2D nonsymmorphic Dirac states. Our result provides a promising material platform for exploring the intriguing properties of essential nodal-line and nodal-point fermions in 2D systems.