Surface electronic properties ofd-band perovskites: Study of theπbands

The surface electronic properties of $d$-band perovskites such as SrTi${\mathrm{O}}_3$ are investigated in some detail using a Green's-function method and a linear-combination-of-atomic-orbitals model developed in our previous work. We consider the nine energy bands ($\pi$ bands) associated with the $t_{2g}$ $d$ orbitals of the cation and the corresponding $p$ orbitals of the oxygen ions. Exact expressions for the local density of states (LDS) of cations and anions at and near a (001) surface are derived and evaluated for a variety of surface conditions. It is found that the LDS of a surface cation is substantially enhanced in the energy range of the filled valence bands when surface states occur in the forbidden band gap. This increase in density results from surface enhancement of the covalent mixing of $d$ orbitals into valence-band wave functions. The surface-enhanced covalency leads to a substantial increase in the number of electrons occupying surface cation $d$ orbitals if intra-atomic Coulomb repulsion is neglected. An approximate Hartree-Fock treatment is employed to investigate the effect of Coulomb repulsion among excess electrons in surface orbitals. Approximately self-consistent solutions for the LDS are obtained. These solutions show that band-gap surface states are forced to lie substantially nearer to the conduction-band edge than predicted by the non-self-consistent theory. Two competing effects arise when the electron occupation is altered on the surface cations. First, there is an increase in the interatomic Coulomb repulsion among the excess $d$-orbital electrons. Second, there is a corresponding decrease in the interatomic Coulomb repulsion (Madelung potentials) because of the reduction in the ionic charges. The intra-atomic Coulomb repulsion dominates for the case of an ideal surface and surface bands are repelled from the midgap region. It is suggested that a surface oxygen vacancy concentration of a few percent can alter the balance between interatomic and intra-atomic Coulomb repulsion resulting in the appearance of band-gap surface bands. These results are employed to suggest a possible explanation of the results of several recent photoemission experiments on the surface states of SrTi${\mathrm{O}}_3$ and Ti${\mathrm{O}}_2$.