Electron-phonon interaction in the lamellar cobaltate NaxCoO2

We study theoretically and experimentally the dependence of the electron-phonon interaction in ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}$ on the sodium concentration $x$. For the two oxygen phonon modes found in Raman experiments, ${A}_{1g}$ and ${E}_{1g}$, we calculate the matrix elements of the electron-phonon interaction. Analyzing the feedback effect of the conduction electrons on the phonon frequency we compare the calculated and experimentally observed doping dependence of the ${A}_{1g}$ mode. Furthermore, due to the momentum dependence of the electron-phonon coupling for the ${E}_{1g}$ symmetry we find no renormalization of the corresponding phonon frequency which agrees with experiment. Our results shed light on the possible importance of the electron-phonon interaction in this system.