Quantized Goos-Hänchen shifts on the surface of hybridized topological insulator thin films

We study the Goos-Hänchen (GH) shift from the surface of a hybridized topological insulator (TI) thin film in the presence of a static magnetic field. We impinge a circularly polarized Gaussian beam on TI thin film substrate and calculate the lateral and angular GH shifts under partial reflection conditions. We show that magnetic field modulated giant positive and negative quantized spatial and angular beam shifts can be obtained by tuning the angle of incidence in the vicinity of Brewster angle and frequency in the terahertz regime. We also investigate the GH shifts in different topological phases of the TI thin film by driving the system through several 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 Zeeman and hybridization interactions. Furthermore, we investigate the effects of chemical potential on the GH shifts. Our results show that the sign of these shifts changes from negative to positive values as the chemical potential is changed from n-type to p-type. The work in this paper sheds important light on controlling GH shifts in different phases of a TI.