Extension of the Brinkman-Rice picture and the Mott transition

In order to explain the metal-Mott-insulator transition, the Brinkman-Rice (BR) picture is extended. In the case of less than one as well as one electron per atom, the on-site Coulomb repulsion is given by U = k rho U-2(c) by averaging the electron charge per atom over all atomic sites, where kappa. is the correlation strength of U, rho is the band filling factor, and U, is the critical on-site Coulomb energy. The effective mass of a quasiparticle is found to be (m*)/(m) = (1)/(1-k2 rho4) for 0 < rho (2) < 1 and seems to follow the heat capacity data of Sr1-xLaxTiO3 and YBa2Cu3O7- at kappa = 1 and 0 < rho (2) < 1. The Mott transition of the first order occurs at rho (2) = 1 and a band-type metal-insulator transition takes place at kappa rho (2) = 0. This Mott transition is compared with that in the d = infinity Hubbard model.