Influence of the spin-orbit interaction in the impurity-band states of n-doped semiconductors

We study numerically the effects of an extrinsic spin-orbit interaction on the model of electrons in n-doped semiconductors of Matsubara and Toyozawa (MT). We focus on the analysis of the density of states (DOS) and the inverse participation ratio (IPR) of the spin-orbit perturbed states in the MT set of energy eigenstates in order to characterize the eigenstates with respect to their extended or localized nature. The finite sizes that we are able to consider necessitate an enhancement of the spin-orbit coupling strength in order to obtain a meaningful perturbation. The IPR and DOS are then studied as a function of the enhancement parameter.