Small-qphonon-mediated unconventional superconductivity in the iron pnictides

Abstract

We report self-consistent calculations of the gap symmetry for iron-based high-temperature superconductors using realistic small-$q$ phonon-mediated pairing potentials and four-band energy dispersions. When both electron and hole Fermi surface pockets are present, we obtain the nodeless ${s}_{\ifmmode\pm\else\textpm\fi{}}$ state that was first encountered in a spin-fluctuation mechanism picture. Nodal ${s}_{\ifmmode\pm\else\textpm\fi{}}$ as well as other gap structures such as ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$, ${s}_{\ifmmode\pm\else\textpm\fi{}}+{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$, and even a $p$-wave triplet state, are accessible upon doping within our phononic mechanism. Our results resolve the conflict between phase-sensitive experiments reporting a gap changing sign, attributed previously only to a nonphononic mechanism, and isotope effect measurements proving the involvement of phonons in the pairing.