Electronic Structure of Disordered Alloys—Iteration Scheme Converging to the Coherent-Potential Approximation

An iteration scheme (referred to as IATA) that repeatedly uses the average-t-matrix approximation (ATA) will be examined. The objective of this work is to devise a computational method which will permit the coherent-potential approximation (CPA) to be applied with realistic alloy potentials. A numerical comparison is made between the IATA and two other schemes which are based on well-known self-energy expressions in a single-band model. The results indicate that among the three methods, the IATA is the only one which converges from the virtual-crystal limit toward CPA for all alloy parameters and for all energies inside the CPA band. However, in concentrated and strong-scattering alloys, especially for minority subbands where ATA is not at all trustworthy, IATA does not converge particularly fast and may produce unphysical structures in the intermediate iterations. A combination of IATA with the extrapolation methods speeds convergence, provides an easy way to achieve the CPA result, and is believed to be useful for calculations on realistic alloys. Finally, an IATA technique for muffin-tin potentials is developed.