Spin Hall conductivity of germanene supported by monolayer of different monochalcogenides and emergence of topologically insulating states

Abstract

Similar to graphene, two-dimensional germanene possesses a honeycomb structure and Dirac cone in its band structure. Being inspired by these similarities, we have studied the electronic structure as well as spin Hall conductivity of germanene supported by monolayers of four monochalcogenides, namely, GaS, GaSe, GaTe, and InSe. By using the first principle calculations based on density functional theory we have investigated the structural stability, buckling of germanene, and electronic band structures of these systems with and without spin–orbit interactions. All the four systems possess Dirac cone in their band structures, but germanene on GaTe and InSe substrates become nonmetallic with very small band gaps of ∼ 28–70 meV. He calculated spin Hall conductivity and the nature of the edge states drive us to infer that germanene, supported by monolayered GaTe or InSe, is a spin Hall insulator with a nontrivial bandgap.