Contribution of the Electron-Phonon Coupling to the Pairing Interaction in LiFeAs

The coupling strengths for intra- and inter-band electron-phonon pair scattering are calculated for LiFeAs. While the sum of these couplings, which gives the total electron-phonon coupling $\lambda$, is of order 0.2, we find that their contribution to the presumed $s^\pm$ superconducting state is reduced by approximately an order of magnitude.