Valley-spin polarization in the magneto-optical response of silicene and other similar 2D crystals

We calculate the magneto-optical conductivity and electronic density of states for silicene, the silicon equivalent of graphene, and similar crystals such as germanene. In the presence of a perpendicular magnetic field and electric field gating, we note that four spin- and valley-polarized levels can be seen in the density of states, and transitions between these levels lead to similarly polarized absorption lines in the longitudinal, transverse Hall, and circularly polarized dynamic conductivity. While previous spin and valley polarization predicted for the conductivity is only present in the response to circularly polarized light, we show that distinct spin and valley polarization can also be seen in the longitudinal magneto-optical conductivity at experimentally attainable energies. The frequency of the absorption lines may be tuned by the electric and magnetic field to onset in a range varying from THz to the infrared. This potential to isolate charge carriers of definite spin and valley label may make silicene a promising candidate for spin- and valleytronic devices.