Raman scattering from the CaC6 superconductor in the presence of disorder

Polarized Raman scattering has been performed on CaC$_6$ single crystal superconductor. We identify two of the three Raman active E$_g$ phonon modes at 440 and 1508\,cm$^{-1}$ expected for the $R\overline{3}m$ space group of CaC$_6$. These first order scattering modes appear along with the D and G bands around 1300\,cm$^{-1}$ and 1600\,cm$^{-1}$ that are similar in origin to the corresponding bands in plain graphite. The intensities of the D and G bands in CaC$_6$ correlate with degree of disorder. The D band arises from the double resonant Raman scattering process; its frequency shifts as a function of excitation energy with $\sim$\,35\,cm$^{-1}$/eV. The double resonant Raman scattering probes phonon excitations with finite wave vector $\emph{\textbf{q}}$. We compare experimental results to from-first-principles calculations.