Pairing and phase separation inBiO3-based superconductors

We study a model proposed before to give rise to a nonconventional pairing mechanism in ${\mathrm{BaPb}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Bi}}_{\mathit{x}}$ ${\mathrm{O}}_3$ and ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$. This model, in which both phonons and electronic excitations play an essential role, is supported by experimental evidence. We solve exactly a ${\mathrm{BiO}}_6$ cluster and we calculate the interaction between this cluster and the rest of the system using perturbation theory in the hopping term. The holes introduced by doping form groups of n holes where n depends essentially on the values of the electron-phonon interaction, Bi-O repulsion, and Bi-O hopping. n=2 is favored near the limit at which the disproportionated ground state becomes unstable.