Elucidating strong coupling between $E_{2g} $ phonon mode and electrons in MgB$_{2}$

Although the isotope effect and the Testardi correlation provide definite proof of the phonon mechanism in MgB$_{2}$, the detailed electron-phonon coupling is not clear yet. For instance, point contact and tunneling spectroscopy experiments show only qualitative information on the (strong) coupling between the $E_{2g} $ phonon mode and the electrons that was predicted by theory. Raman scattering and inelastic x-ray scattering demonstrate the anomalously damped and broad $E_{2g} $ phonon mode due to strong electron-phonon coupling. We follow the change of the anomalously broadened linewidth of the$E_{2g} $mode as the system becomes disordered by impurity substitution and/or ball milling. We expect that the broadening due to the electron-phonon coupling will decrease significantly when T$_{c }$ is reduced to zero due to weak localization. We combine Raman scattering and resistance ratio data to clarify the importance of the coupling between the $E_{2g} $ phonon mode and the electrons in MgB$_{2}$.