Optical spectral weight for the magneto-optical conductivity of topological spintronic semiconductors

The Fermi velocity (v_F) associated with the spin-orbit coupling is two orders of magnitude smaller for spintronic semiconductors than it is for topological insulators. Both families can be treated with the same Hamiltonian which contains a relativistic (Dirac) linear in momentum term proportional to v_F and a nonrelativistic quadratic contribution with Schrödinger mass (m). We find that the ac dynamic longitudinal and transverse (Hall) magnetoconductivities are strongly dependent on the size of vF. When the Dirac fermi velocity is small, the absorption background provided by the interband optical transitions is finite only over a very limited range of photon energies as compared with topological insulators. Its onset depends on the value of the chemical potential (μ) and on the magnetic field (B), as does its upper cutoff. Within this limited range its magnitude is, however, constant and has the same magnitude of e²π/(8h) as is found in topological insulators and also in graphene noting a difference in degeneracy factor.