Electron-phonon interaction in two dimensions: the case for strong coupling in high-Tc superconductors

A particular model interaction between electrons and acoustic phonons is found to cause electrons to become weakly "self-trapped" for an arbitrary filling factor in d=2, but not in d=1 nor, for different reasons, in d>3. To the extent that electron kinetic energy is reduced in d=2, the electronic interactions become proportionally more effective. Among phonon-mediated interactions we identify a static anisotropic interaction, compatible with observed ordering of oxygen vacancies along privileged axes in YBa2Cu307-x, while other mechanisms encourage electron pairing and superconductivity.