Raman spectra of MgB$\mathbf{_2}$ at high pressure and topological electronic transition

Raman spectra of the MgB$_2$ ceramic samples were measured as a function of pressure up to 32 GPa at room temperature. The spectrum at normal conditions contains a very broad peak at $\sim590 \,$cm$^{-1}$ related to the $E_{2g}$ phonon mode. The frequency of this mode exhibits a strong linear dependence in the pressure region from 5 to 18 GPa, whereas beyond this region the slope of the pressure-induced frequency shift is reduced by about a factor of two. The pressure dependence of the phonon mode up to $\sim5 \,$GPa exhibits a change in the slope as well as a «hysteresis» effect in the frequency vs. pressure behavior. These singularities in the $E_{2g}$ mode behavior under pressure support the suggestion that MgB$_2$ may undergo a pressure-induced topological electronic transition.