The impact of inversion and mirror reflection symmetry on Raman scattering of $T' $transition metal dichalcogenides*

Distorted octahedral ($T')$ transition metal dichalcogenides (TMDCs) are topologically interesting material systems. Inversion-symmetry-broken bulk $T'$-TMDCs are predicted to be type II Weyl semimetals and inversion-symmetric monolayer (1L) $T'$-TMDCs are shown to be 2D topological insulators. In this talk, I will show that both the inversion symmetry and the mirror symmetry are important for understanding the lattice dynamics and Raman scattering of $T'$-TMDCs. The mirror plane that is perpendicular to the zigzag transition metal atomic chain classifies lattice vibrations into z-modes and m-modes where `$z$' stands for zigzag and `$m$' stands for mirror. Raman active $z$- and $m$- modes can be experimentally determined with light-polarization and crystal angle-resolved Raman tensor analysis. We report observation of all 9 even-parity zone-center phonons in 1L-$T'$-MoTe$_{\mathrm{2}}$. In bulk $T'$-MoTe$_{\mathrm{2}}$, we monitor inversion symmetry breaking with the shear lattice vibrations, which is important for supporting Weyl fermions.