Unconventional pairs glued by conventional phonons in cuprate superconductors

It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local in space providing unconventional Cooper pairs with a nonzero orbital momentum already in the framework of the conventional BCS theory with weak EPI. In the opposite limit of strong EPI rotational symmetry breaking appears as a result of a reduced Coulomb repulsion between unconventional bipolarons. Using the variational Monte-Carlo method we have found that a relatively weak finite-range EPI induces a d-wave BCS state also in doped Mott-Hubbard insulators or strongly-correlated metals. These results tell us that poorly screened EPI with conventional phonons is responsible for the unconventional pairing in cuprate superconductors.