Density of states of the one-dimensional electron gas: Impurity levels, impurity bands, and the band tail

The density of states of cylindrical quantum wires is calculated in the presence of charged impurities located in the center of the wire. A multiple-scattering approach (Klauder's fifth approximation), which represents a self-consistent t-matrix approximation, is used. For small impurity densities and in the weak screening limit the ground-state impurity band and four excited-state impurity bands are obtained within our approach. We find good agreement between the numerically obtained spectral densities with the corresponding analytical spectral densities calculated with the single-impurity wave functions. The merging of impurity bands is studied. For large impurity densities we obtain a band tail. We present an analytical expression for the disorder-induced renormalized band-edge energy in the band-tail regime.