Electrically tunable Goos-Hänchen shift in two-dimensional quantum materials

We theoretically investigate the tunable Goos-Hänchen (GH) shifts in silicene subjected to an external electric field and circularly polarized light. The prominent feature of these 2D quantum materials is the tunable bandgap that can be tuned by an external electric field or by irradiating circular polarized light beam. Using angular spectrum analysis, we obtain the analytical expressions for the spin and valley polarized spatial and angular GH shifts. We find that tuneable giant spatial and angular GH shifts exhibit extreme values near Brewster’s angles and away from the optical transition frequencies in the silicene. We demonstrate that both positive and negative giant GH shifts can be achieved in the graphene family by tuning the electric field and circularly polarized light in distinct topological regimes. Due to the topological properties of these materials, the GH shift is sensitive to the coupled spin and valley indices of the Dirac fermions as well as to the number of closed gaps. We further demonstrated that topology and spin-orbit interactions play a crucial role in beam shifts and topological quantum phase transitions of the silicene can be comprehensively and efficiently probed through GH shift at the nanoscale.