On the equivalence of Peierls and Holstein models in perovskite structures

We consider the effects of electron-phonon coupling in a perovskite ABO_3, modelled in terms of uncorrelated s-orbitals on the B sites that hybridize with ligand p-orbitals at the O sites. Both the s-p and the p-p hopping matrices are modulated by vibrations of the O, described as Einstein optical phonons. For a single B0_6 cluster, we show that the effects of this Peierls electron-phonon coupling are described well in terms of an effective Holstein model, which couples the carrier to the single "molecular" phonon with A1g symmetry. For a single polaron in an infinite crystal, however, we demonstrate that the Peierls model has sharp transitions as the coupling is varied, where the ground-state momentum jumps between different high-symmetry points of the Brillouin zone. Such transitions are impossible for a Holstein model, showing that there are regions of the parameter-space where the two types of models are not equivalent.