Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of perturbed and pristine PbBiI using the linear combination of atomic orbitals and the Kubo formula. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, spin Berry curvature and spin Hall conductivity are investigated in terms of various parameters. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in PbBiI requires the use of external magnetic fields or magnetic materials.