Single-polaron properties for double-well electron-phonon coupling

We introduce a new model to describe electron-phonon coupling in systems such as one-dimensional intercalated chains or two-dimensional $\mathrm{CuO}_2$ planes, where symmetry dictates that the linear coupling term vanishes. We show that, under certain conditions, an additional charge carrier dynamically changes the local lattice potential from a harmonic well into a double well. We use the Momentum Average approximation to study the properties of this model in the single-polaron limit. A detailed analysis reveals that despite some qualitative similarities to the linear Holstein model, a renormalized Holstein model cannot account for all of the physics of the double-well model.