Abstract
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.
Highlights
The topological phase transition has attracted great attention, for its fundamental scientific importance and for its potential applications [1, 2]
By analyzing the Hamiltonian, we have demonstrated that the topological phase diagram, which is described by GH effect, is consistent with the one described by Dirac mass
The topological number, including Chern number and spin-Chern number, can characterize different topological phases, and they are indicated in topological phase diagram
Summary
The topological phase transition has attracted great attention, for its fundamental scientific importance and for its potential applications [1, 2]. As a two-dimensional topological insulator, topological phase transitions in silicene can be modulated by external electric field and/or irradiating circular polarized light. The interaction of external electric field and/or circularly polarized light with silicene makes Dirac mass controllable, which leads to topological phase transition. It has been demonstrated that the beam shifts in GH effect are very sensitive to the quantized Hall conductivity of graphene in quantum Hall regime [18]. The optical conductivity and Dirac mass are used to depict topological phase diagram. Chern number and spin-Chern number have been calculated Both optical conductivity and reflection coefficient have a very close relationship with Chern number. By regulating external electric field and/or irradiating circular polarized light, topological phase transition will occur. Since the transitional GH effect has a corresponding relationship with different topological states, we believe that this work provides a convenient scheme for directly optical measurement of the different topological features
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