In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{F}}_x$ using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant $\lambda =0.21$ and logarithmic-averaged frequency ${\omega }_{\ln }=206\mathrm{K}$ give a maximum $T_c$ of 0.8 K, using the standard Migdal-Eliashberg theory. For the $F$-doped compounds, we predict even smaller coupling constants. To reproduce the experimental $T_c$, a 5–6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.

• Received 18 March 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.026403