Slave-boson mean-field theory of the Mott transition in the two-band Hubbard model

We apply the slave-boson approach of Kotliar and Ruckenstein to the two-band Hubbard model with an Ising like Hund's rule coupling and bands of different widths. On the mean-field level of this approach we investigate the Mott transition and observe both separate and joint transitions of the two bands depending on the choice of the inter- and intra-orbital Coulomb interaction parameters. The mean-field calculations allow for a simple physical interpretation and can confirm several aspects of previous work. Beside the case of two individually half-filled bands we also examine what happens if the original metallic bands possess fractional filling either due to finite doping or due to a crystal field which relatively shifts the atomic energy levels of the two orbitals. For appropriate values of the interaction and of the crystal field we can observe a band insulating state and a ferromagnetic metal.