Atomically Thin Obstructed Atomic Insulators with Robust Edge Modes and Quantized Spin Hall Effect

protected edge states serve as direct evidence of nontrivial electronic topology in atomically thin materials. Finding these states in experimentally realizable single-phase materials presents a substantial challenge for their use in fundamental studies and developing functional nanoscale devices. Here, we show the presence of robust edge states in phosphorene and group-Va monolayers with puckered lattice structures. By carefully analyzing the symmetry of the atomic sites and edge mode properties, we demonstrate that these atomically thin monolayers realize recently introduced obstructed atomic insulator states with partially occupied edge modes. The obstructed edge modes attain a Rashba-type spin splitting with Rashba parameter (alpha) alpha ) of 1.52 eV & Aring; for arsenene. Under strain or doping effects, these obstructed insulators transition to a phase with substantial spin-Berry curvature, yielding a double quantum spin Hall state with a spin Hall conductivity approximate to 4 e 2 h . The experimental availability of phosphorene and other group-Va monolayers could enable verification of obstructed atomic states and enhanced spin-Berry curvature effects discussed in this study, offering the potential for in electronic and devices.