Optical signatures of the tunable band gap and valley-spin coupling in silicene

We investigate the optical response of silicene and similar materials, such as germanene, in the presence of an electrically tunable band gap for variable doping. The interplay of spin-orbit coupling, due to the buckled structure of these materials, and a perpendicular electric field gives rise to a rich variety of phases: a topological or quantum spin Hall insulator, a valley-spin-polarized metal, and a band insulator. We show that the dynamical conductivity should reveal signatures of these different phases which would allow for their identification along with the determination of parameters such as the spin-orbit energy gap. We find an interesting feature where the electric field tuning of the band gap might be used to switch on and off the Drude intraband response. Furthermore, in the presence of spin-valley coupling, the response to circularly polarized light as a function of frequency and electric field tuning of the band gap is examined. Using right-and left-handed circular polarization, it is possible to select a particular combination of spin and valley index. The frequency for this effect can be varied by tuning the band gap.