Goos-H\"anchen shifts due to 2D materials with complex conductivity

We investigate theoretically the Goos-H\"anchen (GH) shift of a p-polarized terahertz beam incident on a 2D material surface with complex conductivity. Taking monolayer graphene to be the model material, we determine the dependence of GH shifts on the Fermi level and incident frequency. Both spatial and angular GH shifts are present. For both GH shifts in general, we find that increasing the Fermi level shifts the incident angle at which the maximum GH shifts arise. Moreover, we see that at higher frequencies, the amount of beam shift decreases with the Fermi level when the incident frequency is changed. At lower frequencies, however, the shift becomes proportional with the Fermi level. Upon obtaining the measurable shifts, the angular GH shift dominates the spatial GH shift given appropriate experimental parameters. Our results may pave the way for these material's use in optoelectronics devices, and fundamentally, to determine properties of 2D materials with complex conductivity.