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Disorder and localization effects on the local spectroscopic and infrared-optical properties of $\mbox{Ga}_{1-x}\mbox{Mn}_x\mbox{As}$

We study numerically the influence of disorder and localization effects on the local spectroscopic characteristics and infrared optical properties of $\mbox{Ga}_{1-x}\mbox{Mn}_x\mbox{As}$. We treat the band structure and disorder effects at an equal level by using exact diagonalization supercell simulation method. This method accurately describes the low doping limit and gives a clear picture of the transition to higher dopings, which captures the localization effects inaccessible to other theoretical methods commonly used. Our simulations capture the rich mid-gap localized states observed in scanning tunneling microscopy studies and reproduce the observed features of the infrared optical absorption experiments. We show clear evidence of a disordered valence band model for metallic samples in which (i) there is no impurity band detached from the valence band, (ii) the disorder tends to localize and pull states near the top of the valence band into the gap region, and (iii) the Fermi energy is located deep in the delocalized region away from the mobility edge. We identify localized states deep in the gap region by visualizing the probability distribution of the quasiparticles and connecting it to their respective participation ratios. The analysis of the infrared-optical absorption data indicates that it does not have a direct relation to the nature of the states at the Fermi energy.