Goos–Hänchen shift in two-dimensional hexagonal materials

Abstract In this study, we examined the Goos–Hänchen (GH) shift of light beams reflected from the surfaces of various two-dimensional hexagonal materials. We employed a generalized Hamiltonian to analytically derive the band structures, longitudinal, and Hall conductivities of these materials. By manipulating the interaction between external electric fields and spin–orbit coupling, we demonstrated that topological phase transitions can be induced in buckled Xene monolayers (MLs), which can be probed through the GH shift. The GH shift exhibits distinct behaviors across different topological phases in these materials, providing valuable insights into their unique characteristics. Additionally, we investigated the valley- and spin-polarized spatial and angular GH shifts in ML transition-metal dichalcogenides upon reflection. We found that both lateral and angular shifts in these materials, as well as in buckled silicene MLs, are strongly influenced by spin and valley degrees of freedom. This sensitivity makes the GH shift a promising tool for advancing research in spintronics and valleytronics.