Electron correlations and metal-insulator transition in structurally disordered systems: General theory and application to supercritical alkali metals

A general theory for treating the metal-nonmetal (M-NM) transitions in structurally disordered systems is developed on the basis of the Hubbard model and on the tight-binding approximation, and applied to alkali metals under supercritical conditions. An extended-chain approximation developed by Ishida and Yonezawa is employed in the ensemble-averaging procedure over all possible atomic configurations. The Green's function is evaluated in the renormalized single-site approximation and related to the electronic density of states. The localization of the states is examined according to both the modified localization function along the line of Economou-Cohen, and the Mattis-Yonezawa criterion. A metal-to-nonmetal transition is shown to take place when the density is decreased or equivalently the average interatomic distance is increased continuously. From the numerical results, it is suggested that the M-NM transition in a structurally disordered system composed of monovalent atoms is attributed mainly to the effect of electron correlations, although the detailed behavior of the transition point is determined by the localization-delocalization mechanism in Anderson's sense. It is also predicted in the zeroth approximation that the M-NM transition in supercritical alkali metals is of the Mott type.