Possibility of a common origin to ferroelectricity and superconductivity in oxides

We describe an extension of a lattice dynamical model for displacive-type ferroelectrics which might be applied to high-temperature superconductors. The model is based on the instability of the oxygen ion ${\mathrm{O}}^{2-}$, dynamically described by an on-site nonlinear electron-ion coupling, and on the valence instability of the cation [e.g., Cu(I), Cu(III)], represented by a nonlinear electron-electron interaction which provides a pairwise coupling of the electrons. The equivalent quantum-mechanical Hamiltonian describes an extended Peierls-Hubbard system. The most important outcome of the model is that a ferroelectric instability is a necessary condition for paired electron states which indicate the possibility of superconductivity. Depending on the strength of the coupling constants, either a ferroelectric or a superconducting state results.