Valley Hall effect in silicene and hydrogenated silicene ruled by grain boundaries: Anab initioinvestigation

We have performed an ab initio theoretical study of the energetic stability and the electronic properties of pristine and hydrogen-adsorbed grain boundaries (GBs) in silicene. We find that GBs in silicene present lower formation energy when compared with their counterparts in graphene. Removing the inversion symmetry, by applying an external electric field perpendicular to the silicene sheet, we verify the formation of valley-indexed metallic states lying along the GBs, characterizing the quantum valley Hall effect (QVHE). Here, we find the maintenance of the QVHE upon the presence of disordered and asymmetric geometries along the GBs. Those metallic states are suppressed upon the adsorption of H adatoms along the GBs. The H adatoms promote an unbalance on the electronic occupation of the unsaturated $\ensuremath{\pi}$ electrons beside the hydrogenated GB rows, giving rise to (i) a net magnetic moment on the Si atoms along the edge sites of the hydrogenated GBs and (ii) an electronic band structure characterized by spin-polarized valley states protected against backscattering processes.