Tailoring topological states in silicene using different halogen-passivated Si(111) substrates

We investigate the band structure and topological phases of silicene embedded on halogenated Si(111) surface, by virtue of density functional theory and tight-binding calculations.Our results show that the Dirac character of low energy excitations in silicene is almost preserved in the presence of silicon substrate passivated by various halogens. Nevertheless, the combined effects of charge transfer into the substrate, stretching of bonds between silicon atoms, and symmetry breaking which originates from van der Waals interaction, result in a gap $E_{g1}$ in the spectrum of the embedded silicene. We further take the spin-orbit interaction into account and obtain its strength and the resulting enhancement in the gap $E_{g2}=2lambda$. Both $E_{g1}$ and $E_{g2}$ which contribute to the total gap, vary significantly when different halogen atoms are used for the passivation of the Si surface and for the case of iodine, they have very large values of $70$ and $23$ meV, respectively. To examine the topological properties, we calculate the projected band structure of silicene from which the tight binding parameters of the low-energy effective Hamiltonian are obtained by fitting. Our results based on Berry curvature and $mathbb{Z}_2$ invariant reveals that silicene on halogenated Si substrates has a topological insulating state which can survive even at room temperature for the substrate with iodine and bromine at the surface. Similar to the free standing silicene, by applying a perpendicular electric field and at a certain critical value which again depends on the type of halogens, the gap closes and silicene undergoes a transition to a trivial insulating state. As a key finding, we see that the presence of halogenated substrate except for the case of fluorine enhances the robustness of the topological phases against the vertical electric field and most probably other external perturbations.