  The common wisdom that the phonon mechanism of electron pairing in the
weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductors leads to
conventional s-wave Cooper pairs is revised. An inevitable anisotropy of sound
velocity in crystals makes the phonon-mediated attraction of electrons
non-local in space providing unconventional Cooper pairs with a nonzero orbital
momentum in a wide range of electron densities. As a result of this anisotropy
quasi-two dimensional charge carriers undergo a quantum phase transition from
an unconventional d-wave superconducting state to a conventional s-wave
superconductor with more 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
(BEC) limit. The conventional 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.
