Frequency-dependent transport properties in disordered systems: A generalized coherent potential approximation approach

To predict transport properties of disordered systems, especially ac transport properties, one has to calculate the disorder average of the correlation of the multiple Green's function at different energies. To avoid brute force calculation, diagrammatic perturbation expansion must be used along with the coherent potential approximation (CPA). In this paper, we develop a theoretical formalism based on the nonequilibrium Green's function that maps the average of the correlation of the multiple Green's function into an average over a single generalized Green's function. After the mapping, this formalism is structurally very similar to the CPA and completely eliminates the need to perform diagrammatic expansion. As a demonstration of our theory, the dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias in the presence of Anderson disorder are calculated by directly taking the disorder average of the generating function of full counting statistics (FCS) within the CPA. Our numerical results on dynamic conductance, frequency-dependent shot noise under dc bias, and frequency-dependent noise spectrum under ac bias show remarkable agreement with that obtained by the brute force calculation. The phase diagram in the frequency versus disorder strength plane has been efficiently calculated using the generalized FCS-CPA method.