Small-q phonon-mediated superconductivity in organic kappa-BEDT-TTF compounds

We propose a new picture for superconductivity in kappa-(BEDT-TTF)2X salts arguing that small- q electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magneto-optic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless regions on the Fermi surface accounting for the experimental signatures of a Fulde-Ferrel-Larkin-Ovchinikov state and it may induce gap symmetry transitions as well.