Electrical conductivity calculations: Structural disorder and the role of degenerate or resonant electron states

Within a single-electron picture and perturbation theory, expressions for the electrical conductivity (exemplified by the Kubo-Greenwood formula) exhibit divergences for degenerate states and states which are near resonance with an ac field. In this paper, we obtain expressions for the conductivity starting with a many-particle approach, and we emphasize the importance of quantum statistics for the expression for the conductivity. For weak topological disorder, the new conductivity expression can be reduced to semiclassical Boltzmann expressions at various levels of approximation. We show that contributions to current from degenerate states in a low-frequency field and states near or in resonance with an ac field are finite. For the ac case, to the first-order change in the degenerate states caused by external field, new components of current with zero frequency and double frequency are predicted. To the first-order change in the states which are near or in resonance with field, zero-frequency, double-frequency and triple-frequency components of current appear. Zero dc conductivity at T=0 K in an intrinsic amorphous semiconductor can be directly demonstrated if we first calculate the change in many-electron wave functions caused by an external field. We show that for an intrinsic semiconductor, the conventional Kubo-Greenwood formula represents the contribution from single-particle excited states.