Polaron and bipolaron formation in a cubic perovskite lattice

The Rice-Sneddon model for BaBiO3 offers a starting point for discussing polarons and bipolarons in a three-dimensional oxide crystal. We use exact diagonalization methods on finite samples to study the stability and properties of polarons and bipolarons. Because polarons, when they form, turn out to be very well localized, we are able to converge accurately our calculations for two-electron bipolaron wave functions, accounting for the Coulomb interaction without approximation. Some of our results are compared with and interpreted by reference to the variational method of Landau and Pekar. We calculate both electronic acid vibrational excitations of the small polaron solutions, finding a single vibrational state localized with the full. symmetry of the polaron, which has its energy significantly decreased at the onset of polaron formation. Both on-site (Hubbard) and long-range Coulomb repulsion are included in the bipolaron calculation, but due to the high degree of localization, the long-range part has only a small influence. For a reasonable on-site repulsion U equal to two times the band width W, bipolaron formation is significantly suppressed; there is a large window of electron-phonon coupling where the polaron is stable but the bipolaron decays into two polarons.