s-wave superconductivity from antiferromagnetic spin-fluctuation model for bilayer materials

It is usually believed that the spin-fluctuation mechanism for high-temperature superconductivity results in d-wave pairing, and that it is destructive for the conventional phonon-mediated pairing. We show that in bilayer materials, due to nearly perfect antiferromagnetic spin correlations between the planes, the stronger instability is with respect to a superconducting state whose order parameters in the even and odd plane-bands have opposite signs, while having both two-dimensional $s$-symmetry. The interaction of electrons with Raman- (infrared-) active phonons enhances (suppresses) the instability.