Spin-Orbit Coupling Effects on the Structural and Electronic Properties of Planar Pentagonal p-MS$_{2}$ (M = Si, Ge, and Pb)

Spin-orbit coupling (SOC) plays an important role in determining the structural and electronic properties of recently proposed two-dimensional planar pentagonal materials. In this work, density functional theory calculations are employed to investigate SOC effects in p-MS$_{2}$ systems (M = Si, Ge, and Pb). Our results indicate that the p-SiS$_{2}$ structure is likely unstable, except for p-GeS$_{2}$ and p-PbS$_{2}$. A detailed j-resolved (total angular momentum) orbital analysis reveals that SOC enhances electronic localization, leading to a slight structural contraction and a reconstruction of electronic states near the Fermi level, this effect becoming stronger for heavier M atoms. While p-GeS$_{2}$ remains metallic, SOC drives a metal-semiconductor transition in p-PbS$_{2}$ and opening a quasi-direct band gap of about 0.475 eV. In addition, the conduction band minimum state of p-PbS$_{2}$ exhibits pronounced anisotropy along the S-S bonds. These findings provide insight into SOC-driven structural and electronic reconstruction in planar pentagonal chalcogenides p-MS$_{2}$ and suggest that p-PbS$_{2}$ may be a promising candidate for gas-sensing applications.