Topological Imbert–Fedorov shifts in silicene

In this paper, we study the topological Imbert–Fedorov (IF) shifts of a light beam reflected from a silicene–substrate system in the presence of an externally applied electric field and circularly polarized beam. Silicene is a topological material and due to the strong spin–orbit interaction has a rich phase diagram. Using the famous Kubo formalism, we derive analytical expressions for the longitudinal and transverse Hall conductivities of silicene. By employing angular spectrum analysis, the analytical expression of the spatial IF shift is obtained. We show that electric field/circularly polarized light beam modulated positive and negative spatial beam shifts can be obtained by tuning the angle of incidence near the Brewster angle and the incident photonic energy in the terahertz regime. Furthermore, we also investigate the IF shifts in different topological phases of the silicene by driving the system through distinct topological quantum phase transitions (TQPTs), i.e., from topologically nontrivial to a semi-metallic state and further to a band insulating state by manipulating the interplay between the electric field and circularly polarized light beam. We believe these results are helpful for developing novel optoelectronic, spintronic, and valleytronic devices and may provide a possible technique for probing Berry curvature, topological Chern numbers, and TQPTs by direct optical measurement.