On spectral density of electronic states in disordered systems

In the present paper, the averaged spectral density of electronic states, 〈?(k, E)〉, has been computed for three-dimensional disordered systems with spherical well type atomic potentials. The formula for 〈?(k, E)〉 is derived by using a realistic perturbational approach that takes propagator modification into account, together with a handy approximation due toBallentine. 〈?(k, E)〉 has been computed for various sets of potential strength and concentration, and the dependence of 〈?(k, E)〉 upon these parameters has been discussed. The motivation behind the computations reported here, is to examine the circumstances under which the electron motion in disordered systems is expected to be almost free electronic. Our principal finding is that a simultaneous existence of weak electron-scatterer interaction-potential and high density of scatterers would tend to make the motion of an electron in a disordered system almost like that of a free one.