Self-Consistent Mean-Field Theory for Interacting Electrons in Three-Dimensional Deformable Lattice

Abstract

The ground state properties are investigated of a three-dimensional many-electron system with short range electron-electron (e-e) repulsion U , site diagonal electron-lattice (e-L) interaction S and half of the unperturbed electronic band width T . Being the system considered as a random four-component alloy with respect to the effective potential for spin up or down electrons and treating the lattice classically, it is possible to calculate ground state properties for any values of parameters: T , U , S and the electron number, With obtained phase diagrams in the T – U – S triangle, we discuss a variety of possible phases, local spin- and charge-densities, phase transitions, band gap width of insulating phase and structural change. The difference in the half-filled electron case and non-half-filled cases is also discussed in connection with the electron-hole symmetry and the different role of e-e and e-L interactions in metal-insulator transition.