Density of states from moments. Application to the impurity band

Abstract

The moments of the electronic density of states of a disordered system described by a tight binding model can be directly computed as a function of the overlap integrals and the local order of the system. Some of the possible techniques for estimating the density of states from its low order moments are discussed. Two methods are particularly emphasized: one using upper and lower bounds for the integrated density of states, the other using a finite continued fraction expansion of the Hilbert's transform of the density of states. The second method seems to be better due to the fact that the continued fraction coefficients rapidly converge towards their asymptotic values. In particular, their behaviour when internal singularities on a band gap appear is analysed.