Polarons in the three-band Peierls-Hubbard model: An exact diagonalization study

We have studied the three-band Peierls-Hubbard model describing the Cu-O layers in high-${\mathit{T}}_{\mathit{c}}$ superconductors by using Lanczos diagonalization and assuming infinite mass for the ions. When the system is doped with one hole, and for λ (the electron-lattice coupling strength) greater than a critical value, we found that the oxygens around one Cu contract and the hole self-traps forming a lattice and electronic small polaron. The self-trapped hole forms a local singlet analogous to the Zhang-Rice singlet in the undeformed lattice. We also studied the single-particle spectral function and the optical conductivity. We have found that the spectral weight, in general, is similar to that found in previous studies where the coupling with the lattice was absent. There is an anomalous transfer of spectral weight but, contrary to those studies, the spectral weight goes to these localized polaronic states. However, this polaronic shift does not seem enough by itself to explain pinning of the chemical potential observed in real materials. The peaks in the optical conductivity are also shifted, according to the polaronic shift, in the single-particle spectral functions. We compare our results to those obtained in inhomogeneous Hartree-Fock calculations and we discuss their relation with experiments.