Localization of Electrons in Certain Random Lattices

The localization of electrons in random lattice is investigated with the Green's function method following Anderson's probabilistic approach. The energy dependence of the critical value ( W /2 V ) c for localization is obtained for a system with a potential fluctuation of width W and a short range type effective transfer energy V . The calculated results suggest that localized states appear preferably in the edges of the energy spectrum, and, with the increase in the ratio W / V , the regions of lacalized states spread toward the central region and finally cover the whole spectrum. Further, in a one-electron scheme, the effect of electron correlations on the localization of electrons is studied as a source of dynamical potential fluctuation. It is shown that electron correlations are quite effective for the electron localization, especially when correlation energy U exceeds static fluctuation width W .