Goos-Hänchen shift in silicene

Silicene has a rich phase diagram, which is due to the strong spin–orbit coupling induced by the buckled structure. In this work, the Goos-Hänchen (GH) shift of silicene in different phases is investigated. By employing the Kubo model of conductivity of silicene and angular spectrum analysis, the analytical expression of GH shift is obtained. Based on the analytical results, a series of numerical simulations are carried out. The results demonstrate that one can acquire a large negative spatial GH shift at the pseudo-Brewster angle when the silicene is in metal phases. When the silicene is in nonmetallic states, the spatial GH shift become positive. For the angular GH shift, no matter what phase the silicene is in, it varies very rapidly and even changes the sign near the pseudo-Brewster angle. This allow us to manipulate the GH effect by controlling the applied external circularly polarized light electric field or magnetic field. We believe that these results are helpful for developing novel optoelectronic devices that base on the GH effect of silicene.