Phonon anomalies within the polar charge density wave phase of the structurally chiral superconductor Mo$_3$Al$_2$C

We employ polarization-resolved Raman spectroscopy to study the lattice dynamics of the polar charge density wave phase of the superconductor Mo$_3$Al$_2$C with structural chirality. We show the phononic signatures of the charge density wave transition at $T^*$ = 155\,K in Mo$_3$Al$_2$C. The detailed temperature dependence of these phonon modes' frequency, half width at half maximum, and integrated area below $T^*$ reveal anomalies at an intermediate temperature $T' \sim$ 100\,K, especially for the low-energy modes at 130 and 180\,\cm-1. We discuss the origin of these phonon anomalies within the polar charge density wave phase of Mo$_3$Al$_2$C.