Electronic Goos-Hänchen shifts in phosphorene

The total internal reflection of a light beam on a surface in classical optics leads to a lateral displacement along the interface plane. This is known as the Goos-Hanchen (G-H) and usually is very weak. Two-dimensional materials are suitable platforms to generate electronic analogies of the G-H shifts. Here, a theoretical study is performed to evaluate the possibility of increasing the magnitude of the G-H effect in phosphorene. In particular, the G-H shifts and the transmission coefficient are studied for electrons crossing different kinds of potential barriers in phosphorene. Here, a transfer matrix approach is used taking into account current conservation and the problem of non-Hermiticity of the envelope effective equation for sharp boundaries. The obtained results show that the G-H shifts are strongly dependent on the type of barrier and incident angle, yet are suitable to be detected as it turns out to be bigger than in graphene.