Giant non-adiabatic effects in layer metals: Raman spectra of intercalated graphite explained

The occurrence of non-adiabatic effects in the vibrational properties of metals have been predicted since the 60's, but hardly confirmed experimentally. We report the first fully \emph{ab initio} calculations of non-adiabatic frequencies of a number of layer and conventional metals. We suggest that non-adiabatic effects can be a feature of the vibrational Raman spectra of any bulk metal, and show that they are spectacularly large (up to 30% of the phonon frequencies) in the case of layer metals, such as superconducting $MgB_2$, $CaC_6$ and other graphite intercalated compounds. We develop a framework capable to estimate the electron momentum-relaxation time of a given system, and thus its degree of non-adiabaticity, in terms of the experimentally observed frequencies and linewidths.