Peierls versus Holstein models for describing electron-phonon coupling in perovskites
Yau-Chuen Yam, Mirko Moeller, G. A. Sawatzky, Mona Berciu
Abstract
We use the momentum average approximation together with perturbative approaches, in the appropriate limits, to study the single polaron physics on a perovskite lattice inspired by $\mathrm{Ba}\mathrm{Bi}{\mathrm{O}}_{3}$. We investigate electron-phonon coupling of the Peierls type whereby the motion of ions modulates the values of the hopping integrals between sites and show that it cannot be mapped onto the simpler one-band Holstein model in the whole parameter space. This is because the dispersion of the Peierls polaron has sharp transitions where the ground-state momentum jumps between high-symmetry points in the Brillouin zone, whereas the Holstein polaron always has the same ground-state momentum. These results imply that careful consideration is required to choose the appropriate model for carrier-lattice coupling in such complex lattices.