Abstract
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 the spin-fluctuation-mediated pairing interaction. Because of Fermi surface topology details, in LiFeAs all the $\mathrm{Fe}\text{\ensuremath{-}}{t}_{2g}$ 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.
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