Theory of optical conductivity for dilute Ga_1−xMn_xAs

We construct a semimicroscopic theory, to describe the optical conductivity of Ga_1−xMn_xAs in the dilute limit, x∼1%. We construct an effective Hamiltonian that captures inside-impurity-band optical transitions as well as transitions between the valence band and the impurity band. All parameters of the Hamiltonian are computed from microscopic variational calculations. We find a metal-insulator transition within the impurity band in the concentration range, x∼0.2–0.3 % for uncompensated and x∼1–3 % for compensated samples, in agreement with the experiments. We find an optical mass m_opt≈m_e, which is almost independent of the impurity concentration except in the vicinity of the metal-insulator transition, where it reaches values as large as m_opt≈10 m_e. We also reproduce a mid-infrared peak at ℏω≈200 meV, which redshifts upon doping at a fixed compensation, in quantitative agreement with the experiments.