Metal-semiconductor transition in the electronic structure of 4f materials: Application to Er₂O₃

The metal-semiconductor transition due to the Coulomb correlation (CC) is described. The method is illustrated with two band structures of Er 2O3, one including and one without CC effects. This is done by inserting a potential U(r) (the occupation potential) into the band structure and the metallic phase appears when U(r)=0. U(r) together with the potentials Vex±(r) produces two different splittings, 4f up arrow /4f down arrow and 4fo/4fe (occupied and empty bands). The potential U(r) does not keep the symmetries of the 4fe states with respect to those of the 4fo ones. Results show that the hybridisation with other extended states modifies the widths of these bands drastically.