Electron correlations and bond-length fluctuations in copper oxide superconductors: Electron versus hole doping

We investigate the nature of the electronic ground state and electron-lattice couplings for doped chains of $\mathrm{Cu}{\mathrm{O}}_{4}$ plaquettes or $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedra. The undoped configuration implies here Cu $3{d}^{9}$ and O $2{p}^{6}$ formal valence states. The results of multiconfiguration calculations on 4-plaquette (or 4-octahedra) linear clusters indicate strong electron-lattice interactions and polaronic behavior of the doped particles, for both electron and hole doping. For certain phases of the oxygen-ion half-breathing distortions a multiwell energy landscape is predicted. Since each well is associated to carriers localized at different sites, the half-breathing displacements induce charge transfer along the chain. In the case of hole doping, the trends found by ab initio multiconfiguration calculations on 4-octahedra clusters are confirmed by density-matrix renormalization-group calculations for a $p\text{\ensuremath{-}}d$, extended Hubbard model with chains of few tens of $\mathrm{Cu}{\mathrm{O}}_{4}$ plaquettes. Under the assumption of charge separation and the formation of $1∕3$-doped stripes, our results seem to support the traveling charge-density wave scenario proposed in some recent contributions for superconductivity in copper oxides.