Analytic evaluation of Kane fermion magneto-optics in two and three dimensions

We calculate and present an analytic form of the magneto-optical conductivity for the gapped low-energy Kane model in two and three dimensions separately. The two-dimensional case maps onto the alpha-T-3 model at a particular value of alpha = 1/root 3. In two dimensions, two chiral sectors exist, between which there are no optically activated transitions. In three dimensions, the extra dimension of dispersion mixes the two sectors so that intra-and intersector transitions can occur. The latter type of transition can be separated out via circular polarizations of light, and it shows a distinct signature in the transverse conductivity.