An inevitable anisotropy of sound velocity in crystals makes the phonon-mediated attraction of electrons nonlocal in space providing unconventional Cooper pairs with a nonzero orbital momentum. As a result of this anisotropy, quasi-two-dimensional charge carriers weakly coupled with acoustic phonons undergo a quantum phase transition from a conventional $s$-wave to an unconventional $d$-wave superconducting state with less carriers per unit cell. In the opposite strong-coupling regime, rotational symmetry breaking appears as a result of a reduced Coulomb repulsion between unconventional bipolarons dismissing thereby some constraints on unconventional pairing in the Bose-Einstein condensation limit. The conventional acoustic phonons, and not superexchange, are shown to be responsible for the $d$-wave symmetry of cuprate superconductors, where the on-site Coulomb repulsion is large.

• Received 2 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.094502