Transport properties of random and nonrandom substitutionally disordered alloys. I. Exact numerical calculation of the ac conductivity

Results of exact computer simulations for the zero-temperature ac conductivity of one-dimensional substitutionally disordered alloys are reported. These results are obtained by (i) solving for the eigenvalues and eigenvectors of a Hamiltonian associated with a specific configuration of 500 atoms on a linear chain, (ii) evaluating the ac conductivity of this configuration by using the Kubo-Greenwood formula, and (iii) averaging the resulting conductivities over 20 to 50 different configurations (the number of configurations depends on the type of disorder). In all cases convergence (i.e., a stable result) was obtained and confirmed by another independent approach (the recursive method). For not too weak disorder (defined precisely in the text), these results exhibit a great deal of fine structure that includes high peaks and gaps where the conductivity vanishes. These features are reminiscent of, and are correlated with, the similar kind of behavior of the densities of states of one-dimensional substitutionally disordered alloys. Thus we find that the fine structure in the ac-conductivity spectra of one-dimensional systems provides a rigorous testing ground for judging the validity of analytic theories for calculating the transport properties of substitutionally disordered systems.