Transitional Goos-Hänchen effect due to the topological phase transitions.

We examine the Goos-Hänchen (GH) effect for a Gaussian beam impinging on the surface of silicene whose topological phase transitions can be modulated by external electric field and/or irradiating circular polarized light. It is shown that both the spatial and angular shifts in GH effect present a sharp jump due to the topological phase transitions. The transitional GH effect can be attributed to transitional optical conductivity, which relates to Berry curvature and Chern numbers. These results can be extensively extended to other two-dimensional atomic crystals in graphene family. We believe that the transitional GH effect may offer a possible way to determine the Berry curvature, Chern numbers, and topological phase transition by a direct optical measurement.