Van Hove Exciton-Cageons and High-T$_c$ Superconductivity: XB: Polaronic Coupling in the Doped Material

Abstract

A purely ionic interpretation of the tilting mode instabilities in La$_{2-x}$A$ _x$CuO$_4$ (A=Sr,Ba) is shown to be not self-consistent: the dominant factor influencing the doping dependence of the interlayer mismatch is the large change in the Cu-O bond length, which in turn leads to a strong electron-phonon coupling. This coupling is closely related to the vHs-JT effect. This new insight clarifies the role of the tilt-mode instabilities. The main JT coupling is {\it not} to these modes, but to the in-plane O-O bond stretching modes which split the vHs degeneracy. However, as these modes soften, they couple to the lower-lying tilt modes, so that the ultimate instability has a finite tilt component. The bond stretch modes have a large, linear coupling to electrons, with clear polaronic effects. A striking result of this is that there will be a large polaronic band narrowing near the vHs, whether or not the vHs is near the Fermi level. This vHs-localized band narrowing provides a natural explanation for the common occurence of extended vHs's.