Peierls Coupling in Multi-Orbital Superconducting Oxides

We study the effects of the Peierls electron-phonon coupling in different multi-band systems. In contrast to the more commonly employed Holstein coupling, which is used in single-band models and is momentumindependent, the momentum-dependent Peierls coupling can explicitly treat coupling to multiple bands. Our results demonstrate the importance of using the Peierls coupling in modelling complex systems

First, we investigate single polaron physics on a perovskite lattice inspired by BaBiO 3 . We find that with Peierls coupling, the ground state momentum of the polaron jumps between high-symmetry points in Brillouin zone as the coupling strength is increased. Because such sharp transitions are not possible in the Holstein model, it follows that it is not always feasible to map the more complex Peierls model onto the simpler Holstein model.

Then we further investigate the nontrivial behaviour brought by the momentum-dependent Peierls coupling by studying the simplest multi-band system, namely the two-band model on a 1D chain. We show that the Peierls coupling leads to a self-energy that is neither local nor diagonal, opposite to the Holstein model. Peierls coupling can also change the orbital character of the lowest band. To explore whether experiments like ARPES can observe differences in the spectral weights corresponding to the two different couplings, we calculate the intensity measured by ARPES. We demonstrate that various components of the spectral weights are weighted by momentum dependent matrix elements, making it hard to identify the sources of momentum-dependence in the measured intensity.

Lastly, we add the Peierls coupling to Emery’s three-band model for cuprates and study its effect on the polaron effective mass. We show that although the hole-phonon coupling strength is moderate to strong, it only causes a negligble increase in the effective mass, indicating that the effective coupling to the magnon-dressed quasiparticle is much reduced by the dressing. We explain the reason for this and describe how to treat the difference between lattice coupling to bare holes versus to correlations-dressed quasiparticles.