Small-q phonon mediated singlet and chiral spin triplet superconductivity in LiFeAs

We report fully momentum dependent, self-consistent calculations of the gap symmetry, Fermi surface (FS) anisotropy and Tc of superconducting (SC) LiFeAs using the experimental band structure and a realistic small-q electron phonon interaction within the framework of Migdal-Eliashberg theory. In the stoichiometric regime, we find the exact s++ gap as reported by ARPES. For slight deviations from stoichiometry towards electron doping, we find that a chiral triplet p_x+ip_y state stabilizes near Tc and that at lower temperatures a transition from the triplet to singlet s+- SC takes place. Further doping stabilizes the chiral p-wave SC down to T=0. Precisely the same behavior was observed recently by NMR. Our results provide a natural and universal understanding of the conflicting experimental observations in LiFeAs.