Electrical and proximity-magnetic effects induced quantum Goos–Hänchen shift on the surface of topological insulator

Abstract We use scattering matrix method to theoretically demonstrate that the quantum Goos–Hanchen shift of the surface on three-dimensional topological insulator coated by ferromagnetic strips is sensitive to the magnitude of ferromagnetic magnetization. The dependence of quantum Goos–Hanchen shift on magnetization and gate bias is investigated by performing station phase approach. It is found that quantum Goos–Hanchen shift is positive and large under the magnetic barrier but may be positive as well as negative values under the gate bias. Furthermore, the position of quantum Goos–Hanchen peak can also be modulated by the combination of gate bias and proximity magnetic effects. Our results indicate that topological insulators are another candidates to support quantum Goos–Hanchen shift.