Non-Mott metal-insulator transition from Hartree-Fock theory

The Mott-Hubbard theory of the metal-non-metal transition is characterized by electronic localization in the non-metallic phase (Mott insulator). In the present approach, we study a non-Mott transition with extended electronic wavefunctions in both phases. A modified version of the Hartree-Fock theory for the paramagnetic jellium is introduced, in which the screening effect on the charge-charge interactions in the metallic phase is calculated self-consistently. The non-metallic phase is described according to the standard Hartree-Fock method, by including a static dielectric constant in the bare Coulombic interaction. At zero temperature, we calculate the difference ?(?) between the energies per electron in the two phases, as a function of the electron density ?. The equation ?(?eq) = 0 determines the phase-equilibrium value ?eq below which the metallic phase is less stable. It turns out that ?eq is a homogeneous function of the gap width Egap, such that ?eq ? Egap3/2 in three dimensions. These results are discussed in connection with the Goldhammer-Herzfeld criterion and with the band overlap picture of the metal-non-metal transition.