Vibrations in the Flat Land- A Study of the Vibrational Properties of the Transition-Metal Dichalcogenides

Calculations of the vibrational properties of the transition-metal dichalcoginides depend critically on the lattice parameters, symmetries of the underlying system, and the non-local dispersive interaction. Here we present phonon band structure calculations, dielectric tensors, elastic tensors, and Born Effective Charges for the transition-metal dichalcogenides $MoS_2$, $MoSe_2$, $MoTe_2$, $WS_2$, $WSe_2$, $NbS_2$, and $NbSe_2$. We systematically investigate the role of the long-range $e^⁻$-$e^⁻$ interaction, spin-orbit coupling, and pseudo-potential approximation, and highlight their importance on the TMD structural and vibrational properties. We find that the phonon spectrum, calculated with the help of a Grimme's D3 non-local Van der Waals interaction depends strongly on the accuracy of the lattice parameters and slightly on the addition of the non-local Van der Waals interaction in the phonon frequency itself. We also find that the sign of the Born Effective Charges on each atom in the Hexagonal TMDs are the opposite of similarly structured compounds. We explore reasons as to why this occurs. Additionally, our calculation of the dielectric tensor and elastic tensor allow us to describe the mechanical properties of the system which are necessary to know for future device applications.