Electron Correlation and Metal-Nonmetal Transition in a Disordered Binary System

Abstract

The metal-insulator transition due to electron correlation and potential fluctuations in a substitutionally disordered $n$-component system, particularly in a binary disordered system, is studied on the basis of the Hubbard model and of the localization-delocalization concept in the Anderson sense. For illustration, the case of $n=1$ is first studied. This is the original Hubbard system of a regular crystal, for which the mobility gap coming from the random distribution of spins is calculated according to the localization function. The existence of the mobility gap alters not only the critical metal-nonmetal (M-NM) density but also the sharpness of the transition in the sense that the critical index of the mobility gap is 1/2, while that of the density-of-states gap is 3/2. It is shown that for reasonably general systems the resonance corrections in the Hubbard approximation modify the effect of the scattering corrections quantitatively rather than qualitatively. It is proved that, when only the scattering correction of the Hubbard theory is taken into account, the problem of treating the effect of electron correlation in an $n$-component alloy with substitutional disorder is reduced to that of treating an independent-electron picture in the coherent-potential approximation for a $2n$-component system. For binary systems with $n=2$, the quasiparticle densities of states are evaluated for various interatomic distances and the localization of the states is examined. Numerical results are discussed with emphasis on the M-NM transition. A possible extension of the method to amorphous systems with topological disorder is mentioned in relation to experiments on the M-NM transition in some metal rare-gas solids.