Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.