Nodal versus nodeless superconductivity in iso-electronic LiFeP and LiFeAs

Nodal superconductivity is observed in LiFeP while its counterpart LiFeAs with similar topology and orbital content of the Fermi surfaces is a nodeless superconductor. We explain this difference by solving, in the two-Fe Brillouin zone, the frequency-dependent Eliashberg equations with spin-fluctuation mediated pairing interaction. Because of Fermi surface topology details, in LiFeAs all the Fe-$t_{2g}$ orbitals favor a common pairing symmetry. By contrast, in LiFeP the $d_{xy}$ orbital favors a pairing symmetry different from $d_{xz/yz}$ and their competition determines the pairing symmetry and the strength of the superconducting instability: $d_{xy}$ orbital strongly overcomes the others and imposes the symmetry of the superconducting order parameter. The leading pairing channel is a $d_{xy}$-type state with nodes on both hole and electron Fermi surfaces. As a consequence, the $d_{xz/yz}$ electrons weakly pair leading to a reduced transition temperature in LiFeP.